Why does it often seem like a long-term settlement of the Israeli-Palestinian conflict cannot be reached? The easy — and false — answer is that one side or the other just doesn’t want peace. That it will stop at nothing until the other side is annihilated. While it is certainly true that some members of each side believe this, the idea that each side is some monolithic entity wanting only one thing is a convenient fiction for spurring hatred, nothing more.
Neither Israel nor Palestine is a unitary actor. The people who make up Israel and Palestine have diverse preferences, in particular over how to address the defining conflict of the era. Like-minded people on both sides join together into factions that then jockey for dominance. Some of these factions on both sides would take peace in an instant if any reasonable offer were made.