I think there are four factors at play here. They’re mixed together in an extremely messy fashion and overlap quite a bit, but they are:
The people on both sides fear for their safety. The Palestinians fear the Israeli government and military taking action against them. The Israeli people fear rocket attacks and raids like the one that just happened. When a populace lives in fear, it leads to -
Extremist groups are in charge. You have Hamas on one side whose stated goal is to kill all Jews. (Not just in Israel, but across the world.) You have the right wing Israeli government on the other side who push for horrible actions against the Palestinians in the name of “safety.”
Foreign interference. Iran on one side is arming/helping Hamas. On the other side, evangelical Christians help the settlers and push the Israeli government because they think Jesus will come back if Israel suffers a big enough attack. (Peace would prevent that attack and stop Jesus from returning.)
A long and bloody history. Both sides remember when they were killed by the other side. Both sides refuse to leave the past in the past and intend on making the other side pay. The problem here is that the cycle of violence never breaks. If you always have to attack because “they did X to us” then they will feel like they always need to attack because you did Y to them. It goes around and around and never changes no matter how much everyone suffers.
How do you untangle this mess? If I knew that, I’d have the Nobel Peace Prize. I wish I did know. I’d set the peace prize aside in a second, tell the world what to do, and stop it all. Unfortunately, I’m no diplomat. (Some of the best diplomats have failed in this arena.) I can see what’s going on, but I have no clue how to stop it.
The best I can think of is that perhaps UN security forces need to move in. Not to attack one side or another, but to keep both sides away from each other. Sort of like the national version of putting two kids who were fighting in time out until things cool down. But again, I’m no diplomat so for all I know that would make things worse.