One logical fallacy I certainly entertain in order to justify eating dairy products is thinking, "Maybe THIS product is was actually made without harm." Like, cows are painfully raped so they keep producing milk, but sometimes they're legitimately pregnant...so THIS yogurt I'm eating today is from a cow that wasn't raped. Or maybe a cow that actually just doesn't have many pain nerves...probably for some other screwed up inhumane reason, but the POINT is no animals were harmed in the making of this breakfast?*
When it comes to animals, this is a numbers game we will certainly always lose. Sure, maybe that cup of milk actually did come somewhat harmlessly in the moment it was taken, but that's a major fluke, and overall, that cow was miserable, and it's feces put a giant carbon trashbomb into our environment. ADDITIONALLY, there are certain things that there are no question about. If you eat chicken, that chicken's beak was cut off while it was alive. Not every 10 or 50 chickens' beaks. Every chicken's beak. If I cut off one dog nose, I'd go to jail. And you'd probably hate me.
*It's funny that we freak out about animals being harmed in the making of art (which is beautiful and lasting), but we're cool with animals being harmed in the making of fast food (which is generally sad and extremely fleeting).