While Westerners like to look for win-win solutions to problems, Arabs look at everything as a zero-sum game - because when the other side gains, their honor of defeating the enemy is taken away.
The Federalist has an article about the same phenomenon:
To understand why Hamas would pursue such a strategy, one has to go back more nearly 70 years, to the founding of Israel in 1947-48 and the collective Arab response. In the late summer of 1947, Abba Eban, who would later become Israel’s first representative to the United Nations and serve as foreign minister during the 1967 and 1973 Arab-Israeli wars, met with Abdul Rahman Azzam Pasha, secretary general of the Arab League. Eban hoped to secure Azzam’s support for a partition of Palestine and a two-state solution. He reasoned with Azzam that, “if there is a war, there will have to be a negotiation after it. Why not negotiate before and instead of the war?”Notice what Azzam said: "There is no shame in being compelled by force to accept an unjust and unwanted situation."
Eban records Azzam’s telling response in his memoirs. The speech, Eban wrote, “has never been canonized as one of the major signposts in Jewish and Zionist history.” It should be. Azzam said:
If you win the war, you will get your state. If you do not win the war, then you will not get it. We Arabs once ruled Iran and once ruled Spain. We no longer have Iran or Spain. If you establish your state the Arabs might one day have to accept it, although even that is not certain. But do you really think that we have the option of not trying to prevent you from achieving something that violates our emotion and our interest? It is a question of historic pride. There is no shame in being compelled by force to accept an unjust and unwanted situation. What would be shameful would be to accept this without attempting to prevent it. No, there will have to be a decision, and the decision will have to be by force.Eban knew that Azzam was being realistic, that Jews would only win their state in the crucible of war, regardless of whether they secured U.N. recognition. During U.N. deliberations in 1947, the Arab states refused to consider either of the two options put forth by the United Nations Special Committee on Palestine. The majority UNSCOP report urged partition, which the Arabs flatly rejected. (After the General Assembly voted in favor of partition, Azzam stormed out of the Assembly hall and declared to the press that “any line of partition drawn in Palestine will be a line of fire and blood.”)
But the minority UNSCOP report called for a federal state in which the Arab province would have veto over immigration to the Jewish province, essentially allowing the Arabs to secure permanent domination over a Jewish minority. The Arabs rejected this option, too. Eban understood the Arabs’ intransigence for what it was: “The only solution they would consider would be the establishment of an Arab state in which the existence of a separate Jewish minority would be ignored.”
Fast-forward to the current crisis in Gaza: Hamas’ leaders are stuck in 1947. For them, nothing has changed since Azzam proclaimed a line of “fire and blood.” The intransigence of Arab leaders nearly 70 years ago is the present-day inheritance of Hamas.
While is seems counterintuitive to Western sensibilities, Israel's continued attempts for 66 years to find a path to peace that would involve compromise on Israel's part is what keeps Arab hopes alive that Israel is weak and can be defeated. This is why Israel's existence is not accepted as an unwanted but permanent fact, and this is what fuels terror. (There is another factor: the value that Israel places on every Israeli life means that Arab terrorists can claim victory for every Israeli they kill, making "victories" much easier.)
For more on the Arab insistence on a zero-sum game, see here and here.