A horrible thing called the Holocaust happened, and we supported finding a permanent home for the survivors and their descendants. As with most nations on the earth (see Africa), the political lines were drawn according to an outsider's prefereces, and this does usually beget problems. However, I don't think berating the US for following histrical precedent is necessary.
Yes, we could have given them a nice plot of safe land in Arizona, but it was decided that they ought to be close to their holiest sites. Now they're surrounded by over a dozen theocratic and military dictatorships who are all dedicated to their destruction. I'd say we have a moral obligation to prevent that from happening.
As for who has the 'real' rights to the area... I'd say the the Israelis have done a decent job of keeping that land with the significant amount of appreciable military victories, which is also how the rest of the world does it. The Palestinians have been kicked out by superior military might. It happens. They have my sympathy for that, as do the American Indians, but I'm not going to advocate that we turn back the hands of time on either score.
It's worth pointing out that the Israelis have been better stewards of the holy sites, too. When the Arabs were in control in Jerusalem, neither Christians, Jews nor many Muslims (Apostates) were allowed near them.
The Israelis, on the other hand, pretty much allow everybody access (for the most part. Exceptions for especailly dangerous situations). This, in spite of the fact that they expose themselves to danger by doing so.
Thank you for a reasoned reply of which I can find nothing to disagree with.
From what I can tell, if Israel didn't exist, these terrorist groups would hate us anyway. Israel just seems to be another excuse to do so. To the terrorists, we are Infidel, the Great Satan, not to mention generally more prosperous than they are. The last is the least important to them, which is why Jihad is more important than their working to improve their living standards.