It is precisely because people insist on their "rights" to breed horses that we have so many domestic horses in the first place.
If we, as human beings could only get over our crazy thinking that we have to breed and breed other species, more and more, and more, never enough to satisfy, and then heck, kill the "surplus."

I have an excess of cats at the moment, because of other people's irresponsibility and cruelty.
I'm not killing them, that's for sure.