Why Israelis support the Gaza offensive

The Isralis are tired of the missles killing their children. If the peoople in the Gaza can't take it, then they should stop utting it out......

Ofcourse Israelis support the war.
You can be sure that they do not enjoy endangering their own soldiers, and that they do not support this attack because they are racists who want to destroy Gaza.
Simply, they support this attack, because right now, Hamas was rapidly building itself up, while refusing to talk peace, and the only option for Israel to protect itself and minimize the looming threat to Israel's existence was to physically go in and stop them.