This is obviously contentious, but common Vegan arguments appeal to current treatment of animals as tantamount to the aforementioned things. The mass murder of animals, they say, is equivalent or worse than the holocaust given the sheer quantity and industrialized brutality of factory farming. They say that exploiting animals for labor or production is the equivalent of chattel slavery of people. They say that production of milk/cheese or other dairy products and the reproduction of animals for consumption in general depends upon forced fertilization, and is thus equivalent of rape.

All of these arguments depend on believing animals are or at least should be treated as equivalent in moral standing to human beings. This is not a universal position, and one that can be incredibly offensive to people who are victims themselves or descended from victims of the aforementioned crimes. Jews don't like having their systematic extermination likened to the killing of animals because comparing us to animals to begin with was one of the justifications for our mass murder. Rape victims frequently feel that part of what makes their experience so uniquely awful is the disregard for their humanity and the complete objectification of their body for which they are synonymous with. Slavery is much the same, though with some importantly different factors that are beyond the conversation at hand.

Again, Vegans genuinely believe in good faith that animals ontologically have, or at least legally deserve, personhood. They don't make these comparisons maliciously, but I think they are missing their audience because they're not engaging at the level where disagreement actually occurs (whether both or either party is aware of it or not). People take offense to the arguments because they come off as minimalization of crimes against humans, they do not evoke the same level of outrage or sympathy as occurs in the mind of vegans. It's sad to watch unfold tbh.

For what it's worth, I do not think all animals deserve personhood. It may be circumstantially the right thing to do to be vegan given the myriad of factors (mass murder/torture of sentient creatures, persons or not; environmental cost; human toll on workers in the industry) but I do not share vegans ontological commitment to personhood for animals. This makes me more offended and less convinced by the above arguments, but I hope I've at least presented them charitably.