Anthropic specifically called out systems "that take humans out of the loop entirely and automate selecting and engaging targets".

I take that to mean they don't want the military using Claude to decide who to kill. As a hyperbolic yet frankly realistic example, they don't want Claude to make a mistake and direct the military to kill innocent children accidentally identified as narco-terrorists.

At least, that's the most charitable interpretation of everything going on. I suspect they are also worried that the sitting administration wants to use AI to help them execute a full autocratic takeover of the United States, so they're attempting to kill one of the world's most innovative companies to set an example and pressure other AI labs into letting their technology be used for such purposes.