They're firing white phosphorous into Gaza City, which is against the rules of war. Nasty stuff, it burns everything it touches, it'll burn you right down to the bone and it won't stop until there is no oxygen or nothing left to burn. It can't be put out with water. Not something you want to be using indiscriminately in one of the most densely populated areas in the world. This is also what they used to attack the UN headquarters, its still burning. Ban Ki-moon was in Israel when it happened and he was pissed.
Some of the UN schools were targeted specifically by Israel after mortars were fired from nearby streets. These are places that some of the more radical groups had wanted gone, and Israel took the bait. But what possible explanation is there for this? They know exactly what this building was and who was there. If there were some militants in the area (which the UN insists is bullshit), I'd expect some bombs to go their way. But to use white phosphorous? Theres no reason for that whatsoever unless they wanted to be absolutely certain that the UN HQ and everything in it was burned to the ground.
Israel hasn't been strictly targeting only Hamas or militant related targets since this started, they've been systematically destroying civilian infrastructure. The way they've conducted this war is completely unacceptable, they're determined not to get bogged down like they did in Lebanon and they don't care how many civilians get killed.