Fallacy #1: Hamas is bombing kindergarden, they are, deliberatly, targetting civilian targets.
Think about it for a minute. They HAVE to resist. They see themselves as an oppressed people by a dominative nation (as they ARE) and want to fight back (isn't the duty of every citizen to rise up against oppressors?). But what means to they have left?
Not much except throwing rockets. Primitive and crude, "fire and forget" rockets with minimal guidance control. People in this thread have said that "they even have timing device to launch the rocket while they are away". Duh, it's called a "fuse". One of the basic in bomb technology. And until they start having high-tech weaponry except what college students could come up with homemade explosives ('cause those Qassad aren't much more advanced than the homemade rockets made for children).
These rockets don't have guidance system. The best you can even do is aim and hope. What can they aim, when you are about 20 kilometers away from anything? I doubt very much Israel give Hamas the location of their military installation. The only (ONLY) thing remaining are cities.
Even if Israel were to reveal the location of their military installation to Hamas, I doubt they would start firing there. And why should they? It would probably be either decoy, or a blatant lie.
So, if you get down to it, you can't blame any resistance fighter (who's right to resist is enshrined in the Human Rights) for doing the only thing he can do to resist.
Fallacy #2: Israel isn't treating the Gaza Strip "that bad"
Israel enforced a blockade of supplies in the Gaza strip for months. No fuel, no food, no medical supplies. They restrict heavily any kind of media access as they wish, so you will be more likely to hear in detail Israel's side of the story, since they have huge censorship policies toward what is said on their territory, even when it comes to foreign media.
Seriously, one side is in total control. I don't give a damn about a country that has absolute control over a territory. I have zero sympathy for the Israeli who are living in the cities bombed and get occasionnally injured, but their main worry is fear. They complain that they are developping psychological trouble. HOW DO YOU THINK THE PEOPLE IN GAZA ARE FEELING?
We talked about what, 150, 160 rockets fired from Gaza (numbers taken from memory)? You have any idea how many more shells and missiles and grenades and mortars were fires in Gaza in the past days? (not really, guess who refuses to say). With those people who don't have access to any sort of medical supplies, the state is crumbling and beginning to collapse. The rule of law is becoming weaker and weaker.
I realise people got killed on the side of the Israeli, and I am sad that it happened. But it's a long shot between grieving for those victims and demonizing Hamas. These people are trying to rally their supporter in a (justified) defence against Israel. Have you seen people in WW2 calling for "Let's fight the Nazi until they give up"? NO. In war, you rally by saying you will crush you ennemy. That's how you inspire your soldiers and give them faith in themselves, because you tell them you will win, and you will win totally.
The way I see it, Israel is in control. They aren't becoming weaker, and they seem to want to have the occupied population to bow down to them and accept the yoke without any protest. And anything that is aimed at fighting that attitude is decried as rascist or terrorism.