This is a huge topic. I'm going to try to give both perspectives to you now, but be aware that there is no way anyone could analyze the entire history leading up to the partition plan without a lot of conflict.

So what I've decided to do for you is sum up the Palestinian/Arab side, then the Zionist/Jewish side, then the view of the wider international community. If you only want the "reasoning", and don't want to understand the history behind that reasoning, I suppose you can search for "Why partition, in the end", and that'll take to you to that short blurb at the end. But since this is a historical sub, and because history is so crucial to understanding the conflict, hopefully you'll read the summary :).

I can, no matter what, never cover in full all of the crucial incidents that occurred and deserve attention in the conflict. I'm going to try to illuminate the ones I believe are most important to the question, and hopefully give a good representation of both sides.

This is roughly 35,000 characters, so be aware it's not short.

The Palestinian/Arab Side

The Actors

There were two main actors in play, each of which was subdivided into further groups, among the Arabs involved. The two main actors were the Palestinians and the Arab nations. These actors were further subdivided. Palestinians (though by 1947 having mostly rejected the following two views) were divided up on the basis of identification as Muslims, identification with pan-Arab ideology, identification by locality, and identification with Palestine as a nation. The general Arabs, on the other hand, were divided up on the basis of their nation-states: Palestinian (which I include as a separate actor, because they weren't really a nation-state), Syrian, Jordanian, Iraqi, Saudi Arabian, and Lebanese. Other states were actors in the conflict, but the above were the main ones contributing to the war effort in 1948, so I'm going to mainly point them out as actors.

Goals of the Arab States

In this case, the Arab states all had varied goals leading up to the partition plan. Egypt wanted control of the Negev, Syria the Galilee, and Jordan Jerusalem and more. Jordan appears to have stood out, because they wanted to avoid having a Palestinian state established, which would lead to further conflict after 1948 between the Hashemites (Jordanians) and Palestinian refugees. But back to our story.

Goals/Causes of the Palestinians

In light of the above, I've only established the goals of the Arab nation-states. The Palestinians themselves, though fractured in many ways as a movement, had some goals of their own. In the 1920s, they held out hope that they would be able to become a part of Greater Syria, and pan-Arabism was briefly the driving force behind anti-Zionist thought. However, this faded in light of the Faysal-Weizmann agreement, which many perceived as providing concessions to the Zionists and a betrayal of pan-Arabism. At the same time, the Syrians (led by Faysal Husayn, who had helped lead the Arab Revolt during WWI that helped topple the Ottomans to some degree) had passed in their Congress a resolution that said, among other things:

We desire full and absolute political independence for Syria within the following boundaries: on the north, the Taurus Range; on the south, a line running from Rafah to al-Jauf and following the Syria-Hejaz border below 'Aqaba; on the east, the boundary formed by the Euphrates and Khabur rivers and a line stretching from some distance east of Abu-Kamal to some distance east of al-Jauf; on the west, the Mediterranean Sea.

We desire that there should be no dismemberment of Syria, and no separation of Palestine or the coastal regions in the west or the Lebanon from the mother country.

As you can see, the Syrians clearly wanted to annex Palestine. Palestinians viewed this with a degree of support, according to the Palestinian press of the time and most sentiments we're aware of. However, there were other pan-Arab movements (ie. the movement to establish a giant Arab state encompassing the Middle East) and movements to keep Palestine as a separate nation. When Faysal Husayn was deposed by the French in July 1920, the movement mostly lost favor in Palestinian thought, and the move towards Palestinian nation-statehood was to grow to be the biggest.

Now, part of the reason the Palestinians claimed they had a right to independence, and not the Zionists, was predicated on the idea that the Zionists were mostly new settlers to the area. The Palestinians had lived there for over a thousand years under Arab rule, why should the rule be ceded to Jews now? Sure, Palestine had never been its own independent state, but does that mean it should be denied that right now? These were common arguments made by Palestinians, who hoped to establish a Palestinian state or adjoin the area to a state like Syria, since it would echo the Ottoman Empire's control of those same areas. However, as time went on, as I said, the movement shifted away from pan-Arabism and towards independence.

The other major factor leading to the idea that Palestine should get independence as an Arab state or be part of an Arab-led state stems from the McMahon-Hussein Correspondences. Prior to WWI, Hussein bin Ali (who was, if memory serves, the Sharif of Mecca therefore responsible for Muslim holy places) had attempted to contact the British to oppose an Ottoman plan for an extension of the Hijaz railway into Mecca, and he'd hoped to get their help in stopping the plan and ensuring he had maximal autonomy. However, they refused. Not even a year later, on the outbreak of WWI and the subsequent entrance of the Ottomans against the Entente powers, the British were more than happy to contact Hussein and begin overtures that would lead to an Arab Revolt. The British, for their part, made many vague promises leading up to the start of the revolt. Hussein also overplayed his ability to gain support among the Arab-nationalist circles in the Ottoman Empire, which the British ended up believing after a Syrian officer defected and told them of how he'd been contacted by Faysal and heard rumors of the rebellion beginning soon.

The British managed to convince Hussein to launch the Arab revolt on the basis of only vague promises. The promises, which appeared to include Palestine, were given from Sir Henry McMahon, the British High Commissioner in Egypt. It appears that McMahon overstepped the rather general guidelines he was given, and made promises that the British would later have to use semantics to avoid. One of those promises included the eventual inclusion of Palestine in an independent Arab state, which would feed nicely into the pan-Arab ideology that Faysal (Hussein bin ali's eldest son) would espouse as leader of Syria before being deposed. At any rate, the Palestinians viewed the McMahon Correspondences as a promise regarding Palestine, while the British managed to make weak semantic claims on the word "district" that would, theoretically, have meant Palestine was not included in the situation. Under this framework, the British proceeded.

Palestinian Grievances

The British, already viewed as having stabbed the Arabs in the back later with the view of reneging on the McMahon Correspondences, later decided to make an agreement with the French, which is known as the Sykes-Picot Agreement. Here, too, the British appear to have reneged on their promises to the French. Having promised to create an international trusteeship of Palestine (though not in the borders we know today, but around Jerusalem and the northern Galilee), the British proceeded to restructure the deal and even protect Faysal in Syria for a time. It was only when they proceeded to finally acquiesce to French pressure and the economic costs of protecting Faysal that the French managed to enter Syria as agreed in the Sykes-Picot treaty, and take control there. So the Palestinians saw the Sykes-Picot agreement as a threat, and insisted on reaffirming the McMahon Correspondences. When the Balfour Declaration, which I'll discuss later, was made in 1917, the Palestinians were once more alarmed. It is at least partly for this reason that they were so adamant on establishing Arab independence, and Faysal attempted to extend control to Palestine from Syria. In light of all the above events, we can enter the events that went a little more closely to the reason for partition.

In a more general sense, Palestinian grievances also included the British reluctance to provide any serious opposition to Jewish immigration into Palestine. This was viewed as collusion with the Zionists against the Palestinians and Arabs, and they didn't take kindly to the apparent playing of favorites. Refusals to restrict Jewish land purchases also played into these problems, as did the refusal to create an Arab governing body that would effectively help lead the Arabs, like the Jews effectively had in the area.

Oh, big topic.

There are many things that both "sides" could claim to prove that the Palestinian territory belonged to them, but ultimately the Partition was the deciding factor. One of the main reasons was the Balfour Declaration. It was written by British Foreign Secretary James Balfour, and it essentially declared Palestine as the official home for the Jewish people.

Now, it should be noted that the British made many promises to both sides, so there was a lot of false information floating around. The Jews felt that Palestine was their birthright biblically, but also wanted to escape major persecution in Europe and Russia (check out the Dreyfus Affair for an example of this anti-Semitism). The Palestinians felt that the Jews didn't have a right to kick them off of their land. As you can see, both sides have merit.

There were many religious and political reasons to partition the area, but the ultimate one was the Balfour Declaration. Right after the partition plan went into effect and Israel was declared a state, Israelis and Palestinians went to war, which resulted in many Palestinian people losing their homes and being displaced. The Partition gave the central area of Palestine to the Israelis and the West Bank and Gaza to the Palestinians. Up until the 1967 War, these boundaries were in place, but since then, the Israelis have occupied much of the West Bank and Gaza is in control by Hamas (not relevant to the question, just a little background).

Source: A History of Modern Palestine, Ilan Pappe.