I rode our old herdsire down a big hill once because he kept trying to push his head under my legs from behind.. Full rut, and I was dosing his ladies.. So, I thought I'll show you! and let him get completely under me...then I pulled my legs up, thinking he'd realize I was heavy.
Nope.
We started off at a trot, but by the time we got to the bottom of the hill, he was at a pretty good sprint. I bailed a little ways up the other side.. He kept going.
It was pretty fun, in an OH SH*T kind of a way.. Dangerous, though...I definitely could have caused him to injure himself.
I've ridden a goat accidentally, as well. I am a short person, and one of our does is pretty leggy. I threw a leg over her to give her some dewormer. She decided to run. There wasn't much I could do, except grab her ear and twist. lol.
I think most goats couldn't handle being ridden on purpose. Not sure about the large breeds. Are they talking about carting? There are plenty of people that train their goats to pull a cart. But this is the large breeds.
Hmmm. Wonder if the lessons are to teach the rider or the goat.
If nothing else it doesn't sound practical. Goats are surely smart enough, but could probably only bear the weight of a child very far without stressing or damaging their bodies? I'm thinking of llamas, which can be trained for riding but shouldn't carry an average sized adult (though I have seen videos of full-grown men riding them -- I think it must not be good for the llama).
That said my buckling of only 3 months or so is SO strong I can barely manage him. He's always slipping through the gate if he thinks food is involved, so milking takes about twice as long as it should with me having to stash the does' grain outside a 2nd gate and generally get a rope on him to lead him back.
This morning he managed to get through the 2nd gate and as I was hauling him away from the food bucket with about the force I'd need to tow a Buick, I told him when he grows up, I AM going to ride him! I think he will be able to carry 3 of me by then, lol!