I think this one already has a name but I haven't heard it.
Making exceptions to the rules, often even one's own rules, for no logical reason.
The simplest example is "If you take the last cookie, you're a jerk. If I take the last cookie, it's because I was hungry"
A good recent example was someone talking about how evil companies create monopolies to gouge people and that's why government needs to regulate the important markets like healthcare and such.
To which I of course ask "Wait...you are against monopolies...so why is it okay when government does it?"
Of course, they never answer that question. Color me surprised!
In a debate about healthcare, I once posed the question "If your mother was dying and you couldn't afford her hospital bills, would you be okay with someone robbing people at gun point on her behalf? Well that's ultimately what you're doing if you support government healthcare."
Most just called that extremist but one individual surprised me by saying "I'd be on the front lines with my shot gun if that were the case." He got REALLY hostile with me when I called him a hypocrite for that, justifying it by saying it's for the sake of his mother here.
The hypocrisy isn't in his intentions, it's the fact that while he says it's okay for him to rob people to save a loved one's life, he's undoubtedly not willing to let anyone else have that excuse.