I think Rabbit is right about the suction caused by not draining. I didn't think of that because I drained the system, and the old pump came off with hardly any effort. First try removing the coolant overflow cap and maybe that will be enough to allow it to move. If that doesn't help, then drain from the bottom of the rad. If you don't drain via the rad, be prepared to get a lot of coolant once the pump finally comes out!