Every government justification for war is based on false premises. This one being that we're trying to capture/arrest someone evil.
Paul and Ted are shooting at each other, since Ted has committed horrible crimes and Paul is trying to free himself from Ted's grip. (Let them be our analogy for Uganda and Kony.) The usual justification for Joe (or, America) to get involved is that Paul needs Joe's help, and if Joe would just get rid of Ted, everything would be perfect. Works very well when you're thinking of governments as people.
But they're not.
A much better analogy would be that Ted commits an awful crime, and Paul fires cruise missiles at Ted, destroying countless blocks trying to get to Ted, who escapes. Joe then gets involved, firing a submachine gun variously down streets hoping to strike Ted. That is a much better analogy for government wars.