Mine is a fairly short question, and actually it is not my strongest argument, because I don't have one. Nonetheless, it is thought provoking.
If there was NOT a global catastrophe of extreme nature, such as the Genesis account suggests, then what force is pushing the plates together/apart?
Remember, an object in motion stays in motion, unless acted on by an outward force. An object at rest stays at rest, unless acted on by an outward force. The plates sliding against each other creates friction, which is an outward force. (This friction is most visible in the form of earthquakes along the plate boundaries; no friction, no earthquake.) This means that friction is in effect slowing down continental activity. Given enough time, activity would stop completely.
Anything that has an end has to have a beginning, so if the motion will eventually stop, that means it had to be started by something. What started continental drift (technically plate tectonics)? Where do the forces come from to repeatedly break up and re-form supercontinents? (Check the wikipedia article on this.)
Anyway, just my thoughts, as a layman high school student, thought up in about 5 minutes, so therefore not immune to error.