Many people today, so-called anti-Zionists and post-Zionists say the only reasonable solution to the conflict is a single, bi-national state from the sea to the river Jordan. Such as a solution today is against the will of the Israeli (Jewish) citizens and also against the will of the PLO, with practically all political parties in Israel rejecting the very thought of such an idea, all besides tiny anti-Zionist parties and some Arab ones.
But in 1947, such a solution was impossible. While both sides did not like the two-state solution and rejected it, it was a solution that could work. This is why the idea survives as a solution for the conflict until today, with the majority of states supporting it and at least the major political parties in Israel.
However, in 1947, both the Palestinian Arabs and the new Arab states of the Middle East, rejected the very idea of a Jewish state in Palestine. They saw the Jewish state building in Palestine as a European imperialist effort, and thought that if they apply enough pressure, the Jews would leave back to Europe. To the Jews that was unacceptable, especially after the Holocaust, as they finally reached the point where they had a land that was their own, with independent institutions, cities, villages, transportation, ports, everything; and they weren't willing to give it up, no matter the cost.
You see X, some people compare the Israeli- Palestinian conflict to racial conflicts like the conflict between blacks and whites in USA or South Africa. That is an ignorant and foolish comparison. Unlike the blacks in America, the Jews and Palestinians never wanted to live together, since they never considered themselves parts of the same nation. Unlike blacks and whites in USA, they did not share the same religion, the same language, the same culture, a joint history, or the most important of all, a will to live together. If you want to compare the conflict to other conflicts, it is more like the Serbian-Bosnian conflict.
This begins the second chapter. As I explained, the Arabs of Palestine and the Arab states united in an effort to eradicate Israel, but they had quite different plans about what happens when they succeed. The Palestinians wanted an independent state. The Arab leaders probably planned to divide the land of Israel between them. The war ends, the Egyptians get the Gaza Strip and impose military rule over it. The young Jordanian king Hussein, however, had different plans for the West Bank. He annexed the West Bank (in it cities like Ramallah, Bethlehem and Nablus), handed out Jordanian IDs to its resident and declared Jordan as the home of all Palestinians and himself as their ruler, in an unbreakable union of the East and West banks of river Jordan. This action of Hussein placed him in a collision course with the leaders of the Palestinian national movement, who denied his rule over the Palestinians.
Meanwhile in Israel, the Palestinian Arabs who found themselves on the Israeli side of the ceasefire border were given Israeli IDs and gradually gained equal rights according to the principles of Israel's declaration of independence. Those people came to be known as "Israeli Arabs" or Palestinian citizens of Israel. The controversial fate of Israeli Arabs continues to be a problem today. While they are excused from military service (customary in Israel), Israeli politicians often demand that they express their loyalty to Israel and stop expressing their solidarity with their brothers across the border (or stop supporting anti-Israeli movements).
At the same time, the Arab states, outraged by the defeat in the war, begin persecuting their Jewish citizens as the national conflict quickly transforms into a religious one. As you said, Infinite Resignation, before the conflict began, the Arab states and the Jews were quite "okay" with each other. Antisemitism in the Middle East and Africa was not as bad as in Europe, and while Jews were discriminated according to Muslim law, many of them reached positions of power and lived well. This quite peaceful setting ended after the war of 1948, as waves of antisemitism spread across the Arab states, among them Morocco, Algeria, Libya, Yemen, and Iraq. Many Jews lost their possessions and were forced to flee, and most found their way to Israel, until then populated by an absolute majority of "Western" Jews from Europe. This speeded up the state's rate of growth and doubled its Jewish population. The forced exodus of "Eastern Jews" is often compared by Israel to the Palestinian refugees who fled and lost their homes during the war, as an indication that not only the Palestinians suffered the consequences of the war.
The 60's were a third chapter in the history of Israel. The world was already divided between East and West, and while Israel gained support from Britain, France and USA, the Arab states of Egypt and Jordan sided with the Soviet Union. The spirit of Arab republicanism spread across the Middle East, with charismatic dictators like Egypt's Gamal Nasser who sought to create a united secular Arab Republic, quite similar to Atatürk's modern Turkey. Even though he failed, his ideas of nationalism and republicanism (and opposition to religious fundamentalism) are probably central to the worldview of many Egyptians today.
In 1964, The Palestinian Liberation Organization, PLO, was founded and recognized by Arab states as the representative of the Palestinian nation, much to the dismay of king Hussein. Ultimately, the PLO gained enough support among the Palestinians of the East bank to attempt to take over parts of Jordan, which caused "Black September" or the Jordanian civil war in 1970.
In 1967, a crisis initiated by Nasser in Egypt and escalating clashes with Syria and Jordan raised the suspicion of Israel that the Arabs states are preparing another round of war against it. This started the Six-day-war, Israel's most successful operation, when within six days Israel drove away the Egyptian and Jordanian forces from Gaza and the West bank and occupied the Golan Hights aka The Quneitra area of Syria and the Sinai desert of Egypt.
This ends my explanation of the third chapter of the conflict. As I said, from 1967 it all gets more complicated.