Plato, Socrates and Aristotle ate meat, so the form of the good allows killing animals for food
What a philosopher ate tells us little about what their philosophy requires. These same thinkers accepted slavery. The Platonic tradition is also split on this: Socrates' ideal city in the Republic eats no meat, and later Platonists such as Porphyry and Plutarch argued against eating animals.
The Platonic tradition grounds goodness in reason and order, not in pain alone. On that view, the moral community is made up of rational beings who can grasp the good. The thinkers who built this tradition reflected on ethics more seriously than almost anyone and saw no injustice in eating animals. That should give pause to anyone who says avoiding animal products follows obviously from any serious account of the good.
The diet of a philosopher is weak evidence about what their ethics permits. Aristotle defended natural slavery, and Athenian society, Plato's included, relied on it. Nobody now treats that as a reason to think the good is compatible with owning people. Personal and social practice often lags behind a philosopher's own principles, and sometimes contradicts them.
The historical picture is also more mixed than the claim suggests. In Book II of the Republic, the first city Socrates describes lives on barley, wheat, olives, cheese, figs, beans and chickpeas. Glaucon mocks it as a 'city of pigs', and meat arrives only with the luxurious, 'feverish' city. Socrates ties that city to the need for more land, then war, then doctors. The Pythagoreans, who shaped Plato's thinking, abstained from meat. Later Platonists went further. Plutarch wrote On the Eating of Flesh. Porphyry wrote a whole treatise, On Abstinence from Animal Food, arguing on Platonic grounds that killing animals for food is unjust. Plotinus was reported to refuse meat. So the tradition does not speak with one voice. Some of its most committed members concluded the opposite of what the claim says.
Aristotle is a different case. He did argue that animals exist for human use. But he was Plato's student, not his follower, and he broke with him on the forms themselves. He cannot stand in for 'the form of the good'.
The underlying idea is that moral concern extends only to rational beings, or to our moral community. That is a real position, and it can be argued for directly. It then has to deal with its own problems. Infants and people with severe cognitive impairment are not rational in the relevant sense, yet almost nobody accepts that harming them needs no reason. Pointing to who held the view does not do that work.
Citing an authority where the authority is outside their field, is not representative of expert opinion, or where the question calls for evidence rather than endorsement. Citing relevant, genuine expertise is not a fallacy: this is about misuse.
How it applies here: Treats the eating habits of famous philosophers as settling what the form of the good permits. It gives no argument from Platonic principles, and it relies on figures whose personal practice, such as accepting slavery, is not taken as morally authoritative elsewhere.
Presenting only the evidence that supports a conclusion while leaving out evidence that tells against it.
How it applies here: Presents Platonism as uniformly accepting meat-eating. It leaves out the meatless healthy city of the Republic, the Pythagorean influence on Plato, and Platonists like Porphyry and Plutarch who argued explicitly against killing animals for food.