It's not really a riding pet peeve, it's more a general horse pet peeve, but I HATE people that breed their mares when they don't educate themselves and just want a cute little baby foal.
I know of a woman who wanted a paint filly, just like the one she bred and then was put down due to breaking its leg. So, after the mare had TWO solid bay colts one after the other, (which both went up for sale almost while they were still covered in amniotic fluid) she should have realised that the sensible thing to do would be to just BUY a bloody paint filly! Humph.
If I ever breed Allie, the bloody foal will be born worth enough money to keep it safe if something happened to me. Only if Allie goes very well in competition, not just because of her top temperament. Only by a really well matched, successful stallion. Ugh.
My other pet peeve is people who won't spring for proper euth, sending their horse to the knackery (slaughterhouse) or worse, the sales, just because they don't want to spring for the vet and/or disposal. Gah!!!