The claim is in various forms:
Carnists will routinely refer to hunting as being the only humane way to obtain meat, or claims about what lions would do, which is in direct contradiction with this claim since hunted animals by definition aren't bred and lions don't breed animals for their consumption. So if one relies on this argument then one cannot rely on the other and vice versa.
Relatively few carnists eat bred meat but oppose fishing, hunting, and otherwise killing or disturbing wild animals. So it would seem as though this is unlikely to be the actual justification that carnists have since it's inconsistent with their actions and beliefs.
Humans have bred dogs for 1000s of years. Does that make golden retriever steaks OK? If breeding for purpose X is Carte Blanche for action X, one should also consider that most dog fighting dogs are bred for that exact purpose. So if this is our justification, to remain consistent, then we have to excuse a whole host of otherwise inexcusable behavior. But most people would agree that breeding cats with thinner bones "so they don't jam up my shredder" then justifies one throwing kittens into a shredder alive.
Selective breeding for traits like "is made of more/tastier meat" doesn't change the amount of suffering an animal undergoes. Frequently the opposite - most animals suffer greatly because their body proportions have been exaggerated. Chickens lay an order of magnitude more eggs than they were meant to, cow udders almost scrape the ground they are so engorged, and bred turkeys suffer under the immense weight of their giant breast, all of which are traits that have been selectively bred. So this argument is actually an argument for veganism, not against it, because the breeding of animals in this fashion itself should be considered unethical.
According to this argument, it should also be OK for two people to have a child explicitly to torture that child for their entertainment. This technically makes any claim of child abuse impossible for any intentional pregnancy, since this child was technically bred for a purpose and therefore one has moral impunity for any proposed action.
This still doesn't address the damage done to the ecosystem, clearing land for breeding these animals, and starvation of food from third-world countries to feed livestock. The eating of cultivated meat for one's entertainment hurts plenty of non-bred animals. Carnists imagine some ideal fictional universe for themselves where one raises a handful of backyard chickens, which doesn't contain all of the collateral damage of our current meat industry but satisfies the requirement of eating only bred animals. But this is representative of essentially no one.