Heck, so-called "natural horsemanship" people can be abusive to their horses, either because they are administering overly harsh correction when nobody is looking or because they are abusing through love.

I know a mare who for several years was a weekend trail horse and it was very clear who was in charge. Any time she didn't want to do something she would pin her ears and kick out and throw a tantrum.

It was obvious that her owner had responded to this with "Well, if she doesn't want to do it, she doesn't have to..."

It took a lot of work to get her to the point of being a useful horse, and even now she will still pull her BS with less experienced riders or people she doesn't know in the hope that she can intimidate them into backing down.

Not enough correction can also be abuse, because it leads to the horse not being useful and then bad things can happen.