The angle that seems to remain uncovered by the other answers is how Palestinians themselves see the issue. Indeed, much of the debate today is framed in terms of the struggle for the territory within the borders of the Mandatory Palestine (imposed by British and French) or the continuity with the ancient peoples that populated the region in ancient times. Yet, did the local population see itself as a homogeneous and distinct group in the territory approximately corresponding to that of the British mandate?
On the one hand, Palestinians are but a part of a larger Arab world, characterized by distinct ethnic identity, culture, language, and history - just like Texans, Yankees and Californians are viewed today as parts of a larger US nation, rather than distinct countries.
On the other hand, Palestinians have strong family and tribal loyalties, not unlike Bosnians, Croats, Serbs and Montenegrins, who think of themselves as distinct groups, despite the attempts to impose on the a common Yugoslav identity.
Clan and tribal identities
Clan an tribal identities are known to have posed serious issue in state-building in the Middle East, notably in places like Jordan or Saudi Arabia, where the tribes could be forged into a semblance of a nation only via strong central power, supported by military force and generous bribes. This was already the case with Sharif Hussein, the leader of the British-supported Arab revolt, who tried to unite various tribes while laying a grand claim on creation of a single Arab state under his own kingship (see McMahon-Hussein correspondence.) This line was followed on a much smaller scale by his son Abdullah, who became the first King of Jordan, although consistently eyeing a greater state that would include the Palestine (or at least parts of it.)
Tribal fragmentation is also a big issue in Egyptian Sinai peninsula, where local affairs are largely run by the Bedouin clans, some allied to the central government and some more or less openly opposing it.
Compared to the Population of Arabian peninsula, Palestinians have been more sedentary, and more cohesive as a group. This was notably manifested in the great role that they played in the history of Jordan, and other middle Eastern countries, acting as a group loyal to their homeland, rather than playing tribal politics. However, there is a continuity in lifestyle and loyalties between the populations in Negev and Gaza and their counterparts in Sinai, across the border which was somewhat arbitrarily imposed by British and later became official Egypt-Israeli border (See Aqaba incident, Rafah: a town divided.) Clan loyalties are also playing a greater role at the current moment, when they are no more subjugated to Hamas.
Greater Syria
In the wake of the World War 1, when the British and French designs for the region were not yet clear, but the Arab revolt had already failed to produce a single Arab state, there was a movement for a single state in a Greater Syria (including modern-day Syria, Lebanon, Palestine/Israel and Jordan). This was mostly exemplified by the short-lived Arab Kingdom of Syria, under leadership of another of Hussein's sons - Faisal. The anti-colonial struggle, that followed expulsion of Faisal and creation of the mandates, was largely aimed at creation of such Greater Syria, that would,incorporate Palestine - this is exemplified by (awkwardly named) Syrian Social Nationalist Party.
Pan-Arabism
Following the establishment of Israel, the expulsion of a significant number of Palestinians, and the Arab world engaging in a war against Israel, the idea of a single Arab state was revived. Palestinians were among the strongest supporters of it, seeing Arab unity as the only force that could dislodge the Zionists from Palestine. Palestinians were among the greatest supporters of the United Arab Republic, and consistent opponents to various attempts to revive the UN partition plan, notably the famous UNSC resolution 242, in the last 30 years has formed the basis of the Israeli-Palestinian peacemaking.
Palestinians for Palestinian state
Consistently with the pan-Arab views, the Palesine Liberation Organization, established in 1964, aimed at liberating Palestine - not at the establishment of the Palestinian state in either parts or all of the Mandatory Palestine. It was only in 1988 that PLO accepted UNSC resolution 242, implicitly accepting creation of a Palestinian state alongside Israel:
The 1988 Palestinian Declaration of Independence included a PNC call for multilateral negotiations on the basis of UN Security Council Resolution 242 later known as "the Historic Compromise",[85] implying acceptance of a two-state solution and no longer questioning the legitimacy of the State of Israel.
It is only at this point that the PLO declared the creation of a Palestinian state, followed by Oslo accords a few years later. There has been much opposition to this move from the point of view of accepting the existence of Israel and giving up Palestinian claims to the Isreali territory - this opposition still exists, as manifested, e.g., by the position of Hamas (even in their softened 2017 charter). From the point of view of the PLO leadership (i.e., Yasir Arafat and those around him), it was likely an inevitable concession in view of the decline of the Soviet power, which until then was the main backer of the Palestinian and Arab fight against Israel (the USSR provided to Palestinians the military, financial and political backing - not unlike that provided to Israel by the US.)
References
Rashid Khalidi, Palestinian Identity
George Antonius, The Arab awakening
Shafiq Al-Hout, My life in the PLO
William L. Cleveland, Martin Bunton, A History of the Modern Middle East
Philip Robins, A History of Jordan
Benny Morris, Righteous victims