> How do people square those 2 ideas?

If you're seriously trying to understand the nuance of the act itself, you should consider reading what is standard issue for law enforcement and military.

"On Killing" by Dave Grossman is a classic.

If you only want to understand and stay in the realm of politics, I don't think you'll ever find a good answer either way. There's hypocrisy in every argument for or against violence. None of that is on the minds of people "in the shit" at that time. All that stuff comes later. As you're well aware, PTSD is no joke.

What I would take away from this is to recognize all the other ways in which we are compelled to act against our own self interest under what are sold as higher moral purposes.

From that perspective, it's not that hard to see how people can treat violence as just another tool. Whether it works is a question of how much those people value life above all else. If you're surprised that's not always the case in every culture, you may want to study that first. Beliefs may devalue life for persistence against a long history of conflict. This is where you may start to find some glimmers of an answer why we in the west sometimes think violence works to get those people to "snap out of it", but it really is ultimately about control of those people or that land at the end of the day.