First, I've read what the others say, they're not experts. Second, the AFH isn't wrong, but neither am I. Third, whatever direction the nose is yawing doesn't change the fact that the wing opposite the ball will stall first and that's the direction you will rotate in the ensuing spin. Gravity hastens the entry if the process starts from a skid, it slows the process if it starts from a slip, but either way you're gong to spin if you don't recognize and recover in time.
dtuuri
You'll be waiting a long time in most trainers power off. Power on, it's still a multiple second thing and relaxing the controls will fix it immediately until you're well over the top. Even then it'll come right out, but you'll be headed the "wrong" direction. Especially to the right.
Someone asked if there was video, I believe Jesse has one on YT at altitude, demonstrating the behavior of a 172.
Henning wasn't wrong really, and neither were you, but one could almost take a nap and wake up and still avoid a power off accelerated stall that'll do an "over the top" from a slip. If you really want to get the job done, power on and a skid to the left and you'll go for a "ride" sooner in a 172. Well, get it started anyway. Relax anything and it'll recover, usually even into the first turn. After that you'll have to poke the opposite rudder.
It's seriously annoying that most folk now don't have any time at all doing spins. It's fun. It's educational. I wish my 182 were certified to do it.
My first instructor had me spin the holy hell out of a 172 and a couple of 150s. Spins to a heading? Total blast. Gives you something to do other than try to count rotations. "Over the top" stuff? Way cool. Usually helped along by judicious addition of power at the "wrong" time after setting up a horribly cross controlled "approach" to a line on the ground well below us by a few thousand feet. Great example of why to get the controls UN-crossed before you go shoving the throttle up and why you'll have to PUUUUSH if you really don't want that mess to get out of hand real quick.
The 150 spins a ton better than the 172, by the way. Better break and faster initial rotation. I am green with envy of those who have aerobatic time in something that will spin properly. Trainers? They really are pretty benign. The first four or five you think things are happening fast, but after that, it's about as interesting as doing a standard 45 degree bank steep turn.
Since there's no real feel of G forces fo speak of in spins unless you're overdoing it during the dive pullout, 60 degree banked steep turns are more interesting from a purely "seat of the pants feel" than spins, and they're fun, too.