In short, not killing the president results in the president killing people. (And those people might be assholes, but murdering them is a punishment that's not proportionate to the crime.) Hence, Satsuki is indirectly responsible for those murders in refusing to do what needs to be done to stop them.
How to kill him? Knock him out first, then kill him twenty four hours after that. Or kill him in some place where he's guaranteed to not find the body. Of course, he can do the same to her. Logically, that's what a battle between the two can escalate towards.