Why don't the Palestinians have a state?
First of all, the Palestinian Arabs do have a state. Its called Jordan. During the League of Nations Mandate period, the land originally set aside by the League of Nations as the Palestine Mandate was supposed to provide for a national home for the Jewish people. The British were given the authority to manage the Mandate and help the Jews make the transition to independence. Instead, almost 80% of the original Mandate land was carved out and arbitrarily made into the Arab country of Trans-Jordan (later renamed Jordan). In all the land of the Mandate east of the Jordan River it was "No Jews Allowed". West of the Jordan, the 20% part of the Mandate, the British restricted Jewish immigration and gradually adopted policies that were more and more pro-Arab. Palestinian Arabs are the majority of the population of Jordan even today.
All of Israel today, and the Jewish lands historically called Judea and Samaria (now the West Bank) plus Gaza are entirely within the 20% slice of the British Mandate left over after the creation of Transjordan. The British Mandate Overview page gives a table with the details of this geographical distribution of the Mandate lands.
In all of the history of the region, there never was a Palestinian Arab state. The Palestinian Arabs are not a distinct people. With very few exceptions, they are a highly mixed group of immigrants from all over the Middle East and even further regions: Assyrians, Persians and Romans from ancient times, Turks, Armenians, Greeks, Albanians, and Italians, Afghans, Kurds, other Europeans including Germans, Bosnians, Circassians as well as Egyptians, Bedouins, Algerians, Sudanese and many others who have been identified in the population. Most of today's inhabitants can trace their history in the Palestine area no further than the early 20th century when many came to Palestine attracted by the Zionist prosperity and, after World War I, the political stability of the British administration of the Mandate.
Palestinian Arabs have been offered the opportunity to create a state many times, starting with plans advanced during the British Mandate which the Arabs rejected. Then the United Nation partition plan of 1947, which brought Israel into existence, included a nation for the Palestinians, but the Arabs rejected it. Over the decades since there has been plan after plan that would bring peace to the region and a state for the Palestinians: all they had to do was let Israel live in peace. Arabs rejected all these plans, up to and including at Camp David in 2000 and Taba in 2001, and kept the armed struggle going.
It should also be remembered that from 1948 to 1967 the land known as the West Bank, historically Judea and Samaria, part of the Land of Israel, was held by Jordan. During that period the Gaza Strip was held by Egypt. There were no "occupied territories", no "settlements" or any of the other excuses used today to attack Israel. But there was also no peace. Palestinians and the neighboring Arab countries continuously attacked Israel and worked for the destruction of the Israeli state. At the same time, there was no call for Palestinian independence or statehood even though it could have been done by Jordan with the stroke of a pen.
On November 15, 1988, a Palestinian state was proclaimed by Yasser Arafat at a meeting of the Palestine National Council in Algiers. This was the second declaration of such a state, the first being at a meeting in Gaza in October 1, 1948 during Israel's War of Independence. Both the Gaza and the Algiers declarations are largely irrelevant today, notwithstanding that the Algiers Declaration received enormous attention at the time. Since the PLO did not control the intended Palestinian territory, it was only a symbolic act.
In all probability there will be an independent Palestinian Arab state some day, but only after the Palestinian Arabs find leadership that is committed to peace with Israel.