As an American with more international exposure than 99% of the population I see the situation in the Middle East with completely different eyes. In essence the United States Government, which supports the will of its people be it right or wrong, permits Israel to carry out anything and everything it does to defend itself from its hostile neighbors. This is because the US public firmly believe that the use of any force as also happened in Iraq and Afghanistan, to get its objective is justifiable.
This is because the American public have no idea of the history of the setting up of the State of Israel from what was Palestine and how it has survived to date. If they knew the truth their attitude would be very different, and the lobby that backs Israel has the power not to let the people know the facts. The position shown to public is that Israel is a Jewish state anointed by God and not challenged by the Christians in the US who are more pro Jewish than pro Arab. An Arab in the view of the average American is an enemy and the Jew is an ally. This is the crux of the problem.
In the current Gaza crisis the Israelis know that they will never get rid of Hamas or the rockets they send over to Israel periodically. They may believe they can reduce the capability of Hamas by bombing Gaza out of existence, which has currently happened. The reality is that the intensity of destruction is directly proportional to the sympathy for Hamas, so I fail to see anything other than punishment and revenge by a powerful force against hapless people who are nevertheless sympathetic to anything and anyone wanting to harm Israel. Why does Israel continue to do this?
My interpretation is that by showing how powerful and destructive they are they will galvanize the world to action, and force a settlement politically on the Palestinians. The Palestinians will be forced to accept even though they may not like it if they are to be prevented from extinction. Israel knows they always will only have one ally in the form of the US and no other. They know no matter what they do they cannot change that fact, so they don’t care for world opinion and therefore just carry on as they know no one can stop them. The power of their army is no match for their enemies and they also have the ultimate capability of nuclear weapons.
As long as they are oppressed and have no escape the Palestinians will become more extreme and Hamas eventually will become the government.