Israel left in 2005, the "blockade" (which ignores the third border with Egypt) started in 2007 after Hamas seized control and Israel found itself with an enemy worse than Fatah despite it's largest since the Sinai withdrawal to exchange land for peace.
Natanyahu "supporting" Hamas was a policy of containment (coupled with recent pre-Oct-7 increase in work permits to Israel amogst other overtures) and which led to the October 7th. Israelis think a ceasefire would result in resumption of containment and eventually another October 7th so no go.
While Egypt physically controls the border Israel decides what and who can move through it.
Nethanyahu supports Hamas (see money transports most recently, but they've done it for decades) to divide and conquer Palestine between Hamas and PA. And a good Boogeyman is always good for staying in power, though he is likely finished.
Hamas was elected as Bush pushed for elections too early as he wanted to solve the situation before his term ended, PA was unpopular due to corruption. When Hamas won the US pushed PA to do a coup which failed, this caused Hamas to take over Gaza completely and push out PA and stopping future elections.
Hamas is certainly the main problem now, but the situation was caused by typical US fuckery, Netanyahu supporting Hamas didn't help either. Others big problems are the apartheid state of Israel and their systematic stealing of land in the West Bank. If what they have in the West Bank is the kind peace that Israel wants then I can see why people are resisting them.