Until 3 days ago I was pretty settled in my view that Hamas is a terrorist organisation using barbaric tactics. Only in the last 3 days has that view changed based on lack of evidence (among much evidence). I am now uncertain, and seeking more evidence.
Fatah was the party that championed a diplomatic solution. They rule the West Bank, which Israel cuts into smaller and smaller pieces (diplomacy didn't work).
Hamas was the party that championed violent resistance. They rule Gaza and promise to get revenge on Israel. They have super-majority support in Gaza. You might think that is stupid, since any attack of Hamas will cause a much worse retaliation by Israel, but this is what the people of Gaza want. Perhaps more than their own lives, they seem to want revenge.
People were on the land before the people of Israel conquered it (they were not "given" the land, they killed people to get it, Caananites and many others as I recall, with some Ark of the Covenant supernatural device, right? ;-). And many people were on it since.
The levant wasn't "pretty deserted". People had been inhabiting it for thousands of years, as you mentioned earlier in your post. From 1881-1903, about 25000 jews immigrated there. From 1904-1914 another 35000 arrived. By 1922, the population was up to 11% Jews and 89% Arabs. That means there were still far more Arabs there even after those waves of immigration. Data from: https://en.wikipedia.org/wiki/History_of_Palestine
I could try to explain their rationale for wanting revenge on Israel, but I couldn't do it justice not being one of them. And it's so cultural that I doubt many of them remember all the stories and reasons themselves, at this point they just do.
:large