I can do my best to explain it, and I will do so with the assumption that people will approach any ensuing discussion in good faith. I'm not going to try and be wikipedia here, rather to just give a high level explanation of *why* a group of people, who were nearly exterminated, are acting this way. It will be very difficult to find the right words that can satisfy people who are very into this, but I will do my best, especially because I don't see a realistic geopolitical view being represented in the comments.
The question is "Why would Israel act like this?"
Israel has offered many times a two state solution. I think in '47, several times in the 90s, and the 2000s. They have all been rejected. The reason is that the Palestinian leadership wants more. How much do they want? They want all of it. "From the river to the sea" is the expression. They have said it over and over again that this is the only thing that matters to them, and they will sacrifice everything to get it.
That is more or less why Israel is doing this. For some, that is enough to explanation and a fair summary, but if you want to understand more details then read on.
The Israelis, obviously, are not going to just leave their country, and so that leaves the Palestinians with war as the only option. And war has happened, like 4-5 times, and each time the invading forces were defeated. Rather than deciding that the welfare of their people is what matters, Palestinian Leadership values complete, total restoration as the only goal and everything they do is to that end.
So, it can be debated from that point of view whether Israel should exist as a country or not. If you however think that Israel should be a country, even a little bit, then you are basically against the Palestinian leadership's raison d'être.
Even then though, I think most Israelis had a hard time believing that this is how it would be forever. Time after time, war after war, they have tried to 'do the right thing' short of just leaving Israel or dying. For example, they were invaded, the fought, the won, and the controlled Sinai, which was part of Egypt. Then they gave it back, and the Egyptians were reasonable and they signed a peace treaty.
The problem is the Palestinian leadership will never do this, and that is what the point of October 7 was. The point of it was to make peace impossible. Remember, just before the October 7th, there were the Abraham Accords. Basically, Saudi Arabia, Egypt, and Israel were take the first step in establishing a new direction for the Middle East, with those countries at the center of it. Boom, then you have the October 7th attack.
Let me take a step back and and try to address some things.
It's important to say that in 2005, Israel already militarily occupied Gaza. The corridor that has been used to smuggle in weapons for the terrorist was locked down. Then, due to international pressure, Israel withdrew from that region, and they removed any Israeli settlements. What happened? Immediately after, Hamas took over and there has not been an election since. Now, there is no governance, all of the money is stolen and funneled into weapons, and they're backed by Iran, along with Hezbollah, the Houthi, etc... and it is Iran who has a strategic interest in dividing influence in the Middle East.
So let me be clear. They don't want peace.
It's a very difficult situation because Israel would 100% prefer peace. The trouble is that they have a neighbor, who controls millions of people, that would rather be destitute and keep fighting than to govern responsibly.
A good analogy would be something along the lines of North Korea, but with a very different military strategy. Hamas uses guerrilla warfare, whereas North Korea is going for the long shot of a nuclear weapon.
The Palestinian Authority is not that different, other than strategy. They're also incompetent and they also want to see Israel eliminated. However, their strategy is to pretend to want peace, so they can negotiate territory, in anticipation of an invasion. How do I know this? Because every time that a two state solution has come on the table, they would only accept borders that were militarily impossibly for Israel to defend.
So there you have it. That is why this is happening. Because the Palestinians have these people as their leadership, and it's such a sunk cost at this point that they have nothing left but to fight for the total eradication of Israel. This is what happens when you lose 5 wars and still don't get the hint.