This is where his thinking breaks down. It’s assuming a logical connection that doesn’t necessarily exist. In cognitive therapy, I think the focus would be on finding alternatives to the “if…then” scenario. I’m also curious how he feels about his fellow soldiers? Were they all murderers? And if so, what kind of punishment do they deserve?
There’s also the “usefulness” approach. Even if the war was a lie, what value is there in him being angry with himself? How does that resolve or change anything? Is there anything positive he can do based on his experience (even something as simple as not supporting future similar wars, or not voting for people who support them).
IANAT, but those are the kinds of techniques that cognitive therapy would use in this situation.
It does sound like he’s dealing with a lot more than just distorted thinking, though. There is probably some serious PTSD involved.