As TFA says, Israel blames Hamas. They consider removing Hamas an existential matter, and Hamas is holding the Gazans hostage.
I'm not trying to excuse, merely explain. It is not mere bloodthirst. It is a sincere (if possibly incorrect) belief that Gaza as a whole poses a sufficiently significant threat that civilian deaths -- even babies -- are an acceptable part of waging war.
CAVEAT: the current Israeli government, and a significant fraction of the public, may in fact be that bloodthirsty. Despite everything I just said, many people also hold some kind of religious belief that this land is their destiny, and that they are justified in claiming it by means I can only describe as "Old Testament".
That is not all Israelis; it is likely not a majority. (Elections are next year.) But even Israelis who bitterly oppose this government are sufficiently fearful of Hamas as to justify brutal suppression of all of Gaza.