At some point I had to ask myself "do we kill them all, or do we withdraw". Israel has to make that choice, too.

Again, that's not the choice Israel has. They don't have the option to "withdraw." Their alternatives are, "do we try to stop the people attacking us, or do we just let them keep attacking us forever." Phrased that way (which is a massive oversimplification of course), the choice is much more difficult.

One common critique of that view is to argue that if the Palestinians were given a state, they would stop attacking Israel. Many Israelis used to believe that, which is why the two-state solution used to have some traction among the Israeli electorate. Now the two-state solution has almost no support in Israel, because they believe that giving the Palestinians a state would not stop the attacks - it would just mean the attackers would use fighter jets and tanks instead of rockets and rifles.

But because Israelis and Palestinians share the same place, Israel cannot "withdraw." Hence, the ongoing conflict.