And that gets back to, who made up the moving with the center thing anyway? Perhaps an oversimplification overglorification of that whole hara thing the Japanese seem so obsessed with? I don't think it was O'Sensei, that's for sure. Oh sure, he mentioned a hara, but did he really say it was a single point or that it operated in isolation?
it's because of the loin cloth thingy where you tied the knot right in front and the back looked like a thong. so when someone grabbed the knot and pull, you have to move or it would be painful (involved high pitch breathing that we called kokyu that sounded like aaaiiiii...yekkiiii *origin of aiki*); thus, the phrase of "move the hara" or "moving from the center" was born (and the less well known phrase "move your ass"). you can say the same thing with Chasity belt for women. in conclusion, moving with your center has nothing to do with aikido, but with fashion runway stuffs (with or without high heels).