One is religious nationalism. There’s a bunch of Jews who beleive in a kind of expansionist manifest destiny for religious reasons. Conversely, Hamas is an offshoot of the Muslim brotherhood. Their goal is to wage jihad, kill all the Jews worldwide, and establish a Muslim theocracracy over all of Israel.
The other is cycles of violence. Both Israel and Palestine are small. On both sides, basically everyone personally knows someone who has been killed, which makes it easier to dehumanize the other side. Security is front of mind for many Israelis. You get a lot of secular center-left Israelis who don’t hate Palestinians, but are more than willing to turn a blind eye to repression by the IDF if they think it means their kid won’t be blown up by a suicide bomber on the bus to school. That repression fuels further attacks, deepening the cycle.
Edit: as an aside, the extremists on both sides have sabotaged peace efforts at various points. Neither a two state solution nor a secular democratic one state solution are acceptable to either group of extremists.
In 1995, for example, the Israeli prime minister, Yitzhak Rabin, was literally assassinated by a far right orthodox Jew for signing the Oslo Accords with Yasser Arafat.