Unraveling the Complexities: The Decision to Split Palestine into Two States
Thankfully, we have a ton of sources from the UN on this very question. Not only were these decisions made in committees that reported back to the General Assembly, but the UN has been very good at digitizing documents and getting them online. The final report of the UN Special Committee on Palestine (UNSCOP) might interest you, though it's long and ponderous. You can see how they got to this conclusion based on this set of documents, handily digitized for us.
Regarding the decision itself, UNSCOP recognized that a single-state solution was probably unworkable given the demographics of the region. In 1947, the Arab population in the territory of modern-day Israel was 1.2 million, while the Jewish population was 600,000. But it was expected, and this did in fact happen, that this gap would rapidly close as Europe's Jews decided to leave permanently rather than resettle. After 1948, Israel gained about 600,000 more citizens, many of them Jewish, and in the decades after saw lower but still significant levels of immigration, especially from the Soviet Union and Eastern Europe. So demographically, while there was a clear Arab majority in 1947, it wasn't overwhelming (over 30% Jewish) and it was very likely that this majority would evaporate in the coming years. An Arab-majority state may not have supported a massive influx of Jewish immigrants, while Arabs would likely not tolerate a Jewish-majority state.
So the decision was made to create two states, neither of which was territorially contiguous, but which at least contained a majority interest for their group. A majority Arab state, with a large Jewish minority, and a majority Jewish state with a large Arab minority. Makes a ton of sense, right?
But then UNSCOP gets into the practical problems. The eastern shore of the Mediterranean is not a nice place outside of a very thin coastal strip, which is the most valuable land. Most of the disputed land is of poor quality, particularly in the south, which is dominated by the Negev desert. The majority of Israel's water comes from its northern areas and the Jordan River valley. Outside of that, the land is water-poor, resource-poor, and challenging to farm, especially in the south. The report of UNSCOP does a good job illustrating the problem:
"The regional distribution of the population of Palestine is of great significance for the Palestine problem. The heaviest concentration is along the whole coastal plain from the Gaza area to Haifa. Galilee, the plain of Esdraelon, and the inland area of the Jerusalem sub-district are also fairly thickly populated. The central hill country north of Jerusalem comprising the districts of Ramallah, Nablus, Jenin, and Besian is considerably less thickly peopled, while to the south of the Jerusalem district in Hebron and especially Beersheba, the population becomes extremely sparse. In the vast area of the Beersheba sub-district, however, there are about 90,000 Bedouin nomads."
So, in the central, most fertile regions, the population is thickest, but in the south, where resources are the most scarce, the population is quite small, and the land is already occupied by a large and culturally distinct minority.
The other main facet of the region which made it hard to split the country was how separated and segregated both populations were in terms of social and economic life, while remaining distinctly interdependent. The report notes that many Jews and Arabs refused to cross the religious boundaries socially and economically, saying that Palestine presents a fascinating [economic] study both because of its rapid development as an area of mass immigration and because of its peculiarities in structure due to the lack of homogeneity between the two major elements of the population.
And regarding what the report calls "economic separateness," it goes on to say:
"Apart from certain parts of the country which are predominantly Jewish and others which are predominantly Arab in population, this 'economic separateness' of the two communities does not correspond to any clear territorial divisions."
So again, the disputed territories were heavily intermixed but totally unintegrated. Both groups relied on each other, but refused to really work with each other. And so division was hard, as was the prospect of creating a two-state solution in which minorities in both states may find themselves shut out of social or economic integration.
The 1948 war destroyed any possibility of a true two-state solution, because it 'solved' the crisis of who controlled what regions. Once blood was spilled taking or protecting a town, there was no backing down from that position. By militarizing the problem, both sides ultimately calcified the borders into an Israel, which had all the advantages of population and position, and a divided Palestine (which was not even administered by Palestinians but by Egyptians and Jordanians!), a rump state which could not exist without outside support. Everything that has come later for the Palestinians has spun off this decision, made mostly by non-Palestinians, to risk their future on a dice roll that lost.
In summary, the decision to split the region into two states was complex and made based on demographic, geographic, and political factors. It aimed to address the interests of both Jewish and Arab populations but ultimately failed to achieve a sustainable solution, largely due to the complexities and conflicts inherent in the region.
What would it mean for a single state to be an "Israeli state" or a "Palestinian state" in those scenarios?
So some key context, as the British Mandate faded out local Palestinian groups began to cement control over certain regions. Jewish residents themselves dislike this, and so revolted (as the Palestinians had likewise revolted against the British, and so on). The Mandate government had empowered local Arab leaders and had passed some tough laws to combat violence. Laws which were used against Jewish settlers after 1945 as the violence shifted into a Jewish insurrection against the Mandate. So a 'Palestinian' state was one in which the leaders who currently administrated with the British against the Jewish revolt was given free reign to maintain their current policy.
An Israeli state would be one in which the Jewish leaders were permitted to take power in a new state, in which the new state would agree to some of the demands of groups like the Haganah, and which would recognize Jewish minority rights and political legitimacy. But would likely also be one the Arabs found unacceptable and thus one they would resume fighting against.
The real question between 'Israeli' and "Palestinian' states was the question over the middle. Who got the regions which were independently split, and thus key to securing political control over the state. Bound up in this was the promise of continued violence if one side felt they were going to be shut out of the political process.
What was the reason why so many countries wanted to exit the area? Was just because they had 2 groups of people who didn't like each other and caused problems? Like, was there ever a consideration that some other powerful country would take over and force the two groups to get along much as how the country was under England's control before the split?
I'm...not sure I'd characterize the British Mandate in Palestine like this. There was severe (and worsening) intercommunal violence during the Mandatory period, including 1921 riots in Jaffa, 1929 riots/uprisings by Palestinians, the 1936-1939 Palestinian Revolt, and the Jewish insurgency of 1944-1948. A big part of why the British withdrew is because they didn't want to be caught in the crossfire any more.
Mandatory Palestine was originally a League of Nations Mandate (ie, territories of the former Central Powers taken over by Entente Powers after World War I). It specifically was a "Class A" Mandate, meaning that its administration was to prepare for independence. Other Middle Eastern Class A Mandates had already achieved independence: Iraq in 1932, Syria and Lebanon in 1945, and Transjordan in 1946. So independence/decolonization was always the stated goal, and once Britain had enough and wanted out, it's not like any other country particularly wanted to take up mandatory administration, given the worsening conflict.
The Ottomans had done just this up until World War One, though Arabs living across the Middle East had in the early 20th century become incredibly unhappy with their Turkish rulers. The history of the Ottomans through this period is really one of collapse and entropy, as Arab rules broke away (in more or less direct ways) from Istanbul's direction. So as far back as the 19th century you have a group of people, both Jews and Arabs, who feel like they ought to rather be independant.
France has similar troubles in Mandate Syria, and the British struggled mightily with Iraq and Persia (though Persia was not at that time a mandate), so the larger context for whats going on in Palestine is that its more complex but nothing new. 'Stepping back in' to the Mandate system doesn't just mean dealing with the Arab-Israeli problem, but probably also solving the issue across the Arab world. And by solving I of course mean reasserting imperial control. The mandate style of government puts a unique twist on it, but ultimately this is a very familiar story of post-war decolonization, where European powers decide that they dont want to keep up the old Imperial system and so try to exit as best the can. In the case of Israel though, the conflict there is very hard to resolve and touches on a ton of other issues, so the break isn't so clean.
Add ON:
The first is that the other user's comment explains the UN proposal for a two-state solution, provided by the UN Special Committee (UNSCOP) that was mentioned. This proposal was adopted by a required 2/3 majority of the United Nations General Assembly in Resolution 181, on November 29, 1947.
Notably, however, this resolution was not implemented. Nor did it have any mechanism for the General Assembly to do so; rather the Resolution itself made clear that it was recommending the implementation of the plan by the UN Security Council.
The second note is that given this split, with the reasons the other answer gave, how did we reach the territorial configuration that most individuals know as the "1967 lines", or the "Green Line"?
The answer to that is simple: war. Following the passage of the UNSCOP proposal being adopted by the General Assembly, Arab militias attacked buses in Jewish areas, and local Arab leaders began calling for a general strike. Jewish leaders were celebrating, but were wary, and indeed expected war. War was not long in coming; following the militia attacks, the violence began to spiral and grow until it reached the status of a full-fledged civil war. As with most civil wars, it did not remain a purely local affair; Arab states contributed arms and funding to local Arab forces, as well as "volunteers" (typically soldiers who were sent in covertly) to assist the local Arab cause. British control was severely threatened and limited to trying to quell the violence near their forces, and quickly devolved into a general decision to withdraw from the area.
The lines were not cemented, however, until 1949. That is because the Jewish forces had largely won the civil war, with the understanding from the British that their Mandate (sovereignty granted by the League of Nations and affirmed by the UN following the Ottoman Empire's demise and end of control over the area) would end on May 14, 1948. On May 15, 1948, Israel issued a declaration of independence, declaring its statehood and sovereignty. It did not pick specific boundaries; while it stated a readiness to assist with implementation of the resolution passed by the General Assembly, it did not explicitly endorse it nor did it ever become implemented. This vagueness was intentional; Israel felt that those borders would be indefensible now that war had already begun and the plan been rejected, so it was reluctant to endorse borders it felt would only have been workable if accepted by both sides.
As such, the lay of the land post-1949 in what is referred to as the "1967 borders" (because they changed after 1967, when Israel won the Six Day War against Egypt, Syria, and Jordan) was not determined by the UN. Nor was it determined by Israel. In fact, it was determined between Israel and various Arab states. Each border was delineated by agreements between Israel and the Arab states who invaded it upon its independence, on May 15, 1948. As the British were no longer in the way, the Arab states now had full ability to invade without violating the sovereignty (which by then largely existed by name only) of the British over the Mandate. While they might encounter some British troops (withdrawal was set to be completed by August 1), they were largely free to invade without risking British ire. Indeed, some local British intelligence agents encouraged the Arab states to invade, though it is unclear how much authorization they had to do so from the domestic British government.
Each line was set up by a separate agreement, as I said. The Israeli-Syrian border was set up by an armistice agreement with Israel and Syria. The same is true of the Egyptian-Israeli border, which also set Gaza as part of Egypt. The same is also true of the Jordan-Israel border.
Interestingly, these agreements were armistices. This is a nuance of law and fact, but armistice agreements serve to provide terms for a cessation of hostilities and fighting; they do not serve as peace agreements. Notably as well, these agreements typically included clauses stating that they were not the finalized borders between the parties. As the Jordan-Israel armistice agreement explained:
It is also recognized that no provision of this Agreement shall in any way prejudice the rights, claims and positions of either Party hereto in the ultimate peaceful settlement of the Palestine question, the provisions of this Agreement being dictated exclusively by military considerations.
This was also bolstered by another provision, stating:
9. The Armistice Demarcation Lines defined in articles V and VI of this Agreement are agreed upon by the Parties without prejudice to future territorial settlements or boundary lines or to claims of either Party relating thereto.
This left the ultimate borders relatively unsettled. Israel would go on to sign peace treaties with both Egypt and Jordan. Egypt had occupied but not formally annexed the Gaza Strip from 1948-67, and maintained control over it until Israel gained it in the Six Day War. Jordan annexed the West Bank, though this was not recognized by most if not all of the international community, until it lost it in 1967 as well. When Israel signed the treaty with Egypt, it set the Israeli-Egyptian border outside of Gaza, and the same was true for its treaty with Jordan. As such, what is typically known as "Palestine" today and its borders is the result of a long and convoluted process originating in a proposal by the UN, but ultimately set by agreements between Israel and its Arab neighbors, and not any external actor nor any agreement between Israel and the Palestinians themselves.