That is a long and complicated answer. I hazard a guess that it is in the interests of 'the West' to have a strong Israel and for there to be no credible threat to the Jewish state. The reasoning behind this being that the establishment of Israel is a Western creation in atonement for their behaviour (pogroms, ghettos, concentration camps and the Final Solution) towards Jewish people over a considerable period. The West has encouraged Jews to move to Israel and has no desire, in the event of a threat to its existence, to be either (a) having to assimilate that quantity of Jewish people back into 'the West' [knowing that anti-semitism is only just under the surface] and/or (b) complicit in Arabs delivering their versions of such Pogroms and Solutions - 'Throwing them into the sea'. Add in that Jewish people have considerable influence in the upper echelons of some Western countries, and (as pointed out in #1168) nobody wants to be labelled anti-semitic (to which there is a very fine line, poorly defined) because of the deep discomfort over the historical actions of 'the West' towards the Jewish people for the 300? years prior to 1945.
Bearing in mind the above, it is all to do with what the Arab world does, and in particular recognition of the right to exist of Israel and as a Jewish state. Until that question is settled there can be no peace. Harsh on Arabs, but pushing the Jews back into the sea is about as likely as Germans getting their ancestral lands in East Prussia back.
I suspect that 'the West' does not really have any choice, because they know Hamas was threatening the security of Israel, and Hamas and Palestinians are not easily separable. They are already way, way in deep - going back to the setting up of Israel in the first place, a creation of 'the West'. But we are where we are. I think it is much deeper and complicated than the surface of the current conflict, and naive to think otherwise.
And yes, this is all a bit harsh on the Arab Palestinians. Their future has been sacrificed by 'the West' from the turn of the last century, in order to try and resolve a vexing problem there. I fully understand the Palestinians viewpoint. Deadlock.