What I was taught (and haven't seen it put quite like this in this thread) is that the names we use for the modes were orginally used for by the Greeks for their modes (which were appearently based on a quarter tone system). The modes we have today however, aren't related in any except by name to the original Greek modes. The reason the modes all can be played on white keys is that when they were created, the black keys didn't exist. If you started on F, you played or sung Lydian. At least this is what was taught in music theory and music history classes.
Ionian is now Major and Aeolian is minor.