Quick answer: They think it belongs to them as their inheritance through Ishmael.
Long answer: It belongs to the real heir, Isaac. The Bible records important dreams, including God’s promises. Abram, later named Abraham by God, got into a royal mess because he took a promise in a dream and tried to make it come true on his own. God promised Abram, then childless, that he would be the father of thousands. The temporary and consequently disastrous solution was to have a child through his house maid. That first son was Ishmael known today as those nations constituting the political religion of Islam. A few years later the 2nd and promised son Isaac, is born – the real heir.
In virtually every society except the USA blessings and rewards go to the eldest son, not the younger. You see the problem. Modern day Islam thinks it is entitled to the entire inheritance from Abraham and willing to strap bombs on their children to force the issue. Islam is avenging itself because of something that happened 3,500 years ago, and the likelihood these people will change their minds is Zero.
The land of Canaan (now Israel, formerly Palestine) goes to Isaac and his descendants, hence the battle over a tiny piece of land no bigger than New Jersey. And Europe who tried to pretend for decades that it was so magnanimous and egalitarian is now on High Alert. Iran, even though it is originally Persian, is also controlled by Islamic leaders and part of the enemies of Israel and the West.
See this map online. Tiny little Israel caught in the middle. Only God can help.