Dont they believe it is theirs to begin with?
Yes, Israel believes it has the rights to the entire Israel. As do the Palestinians. Israel has offered time and again to compromise, often to the point of shooting itself in the foot with indefensible borders. The Palestinians have turned them down time and again (see 1949, Oslo accords, Olmert offer). The Palestinians have never even acknowledged Israel's right to exist.
But yeah, there is a peace process.