Sure, but even conservative governments can have progressive policies. Not everything is totally left and right like it seems to be in the US. I don't think I've ever argued otherwise.
Secondly, nobody is rooting for HAMAS to win, not even those opposed to the war. It's a fallacy to think that if Israel, who has the strongest military in the middle east, who is also backed up by the strongest military in the world, is suddenly going to be vulnerable and destroyed by a rag tag bunch of terrorists.
Its just not, but a ceasefire will at least allow for civilians who need go evacuate to get out of Gaza, or get the aid they so desperately need.
Israel is going to beat HAMAS regardless what happens, but why allow pointless suffering to be conducted when Israel can put innocent civilians as their first measure of protection? On both sides.