Most people don't use critical reasoning to make their decisions, hence why most people live their lives in a state of constant contradictions.
My old philosophy professor once told us that the most effective way to expose somebody's lack of critical reasoning about an issue is to just respond with, "who says?"
Basically the Socratic method, ask them to justify the statements they make, and see how they respond. The vast majority of the time, you'll quickly find out that they don't have any good reasons to support their statements. They haven't given them much thought at all, nor much thought to differing views/positions. They live their lives in ways that feel generally "correct" or pleasurable to them, and that's it.
Why do they think it's alright to eat factory farmed meat? Because they like the taste, the thought of billions of animals living short, miserable lives, then being slaughtered and processed for us to consume doesn't horrify or disgust them, so they keep doing it.
Most people when challenged on it will put up some vague attempt to support their actions, "Other animals do it to each other, so why not us?" "Animals don't have sophisticated minds, so it doesn't actually cause them real suffering." "Humans need animal protein to be healthy." etc. All terribly weak arguments that are easily refuted. But most people don't care, because most societies normalize meat consumption and factory farming. They grew up eating meat with other people eating meat all around them, and they never gave it any thought.
Hence why most pet owners who eat meat would be absolutely horrified and disgusted if their dog or cat had a litter and somebody bought all of the puppies/kittens, only to torture, slaughter, and eat them. A completely inconsistent reaction given the fact that the pet owner happily eats other animals that are treated in the same way. But again, they didn't reason themselves into their viewpoint, so they don't worry about being consistent.
This is further confirmed by anecdotes from vegetarians/vegans, who will tell you about all the awkward, unprompted reactions from meat-eaters when they find out they don't eat meat. Many people get very defensive, often making snide or accusatory remarks about vegetarianism/veganism. They don't like the idea that eating factory meat is morally wrong, because they like the taste and don't want to make to effort to change their lifestyle to confirm with that moral principle. So they mock, tease, or try to "expose" inconsistencies in the vegetarian/vegan's own worldview as a defense mechanism.
If they can make the vegetarian/vegan look foolish, then that feels like a win psychologically to them, which provides mental and emotional comfort and allows them to slip back into their lifestyle without needing to confront their own moral failings.