Your essay was one of the better ones I've seen written by a youth, even though I agree with some of the others that it's definitely very one-sided and has some rogue apostrophes (sorry, but I'm a teacher's kid...)
From the perspective of some of us, I'd like to suggest that there are a few questions unanswered by your solution to have the breeders stop breeding.
For example, has this solution already been suggested? Tried? Was it successful? Why or why not? If not, what next? Can it be determined whether the suggested solution to the problem is likely to succeed if certain conditions exist? If so, what conditions are needed?
Also, you could explore the question of "what if slaughter goes away altogether?" There are lots of issues there, and I don't recall any solutions presented in the essay for those horses that you agreed shouldn't be left starving and unclaimed or unwanted in the US, Mexico and Canada.
And the next and last question I'll suggest to prompt the critical thinking process is to ask what would happen if slaughter was banned not just for horses, but next for other meat animals. I'm the first one to agree that humane treatment must be required for animal husbandry, but the US Humane Society has an agenda that is not consistent with providing affordable, nutritious protein, milk and eggs for people to eat. They and other groups would like to see all animal farming and slaughter stop.
Good luck - you can still flesh out these opposing thoughts and opinions, and then conclude with your view, just like your teacher allows. But by fleshing it out, you'll educate others in a more balanced way, might actually prompt a discussion that yields solutions in your circle of influence, and you'll gain respect for your research.