Good debate. It always strikes me as funny when people try to reduce a philosophy to absurdity by showing it entails human extinction (or the extinction of all sentient life), because I genuinely believe that extinction is ideal. I agree with Rhys that if veganism is necessary, there are far-reaching consequences that most people don't consider, but immediate human extinction may not be a consequence. In this essay, AntiBullShitMan argues:

Had human beings gone extinct in the early 1970s, there would be roughly twice as much sentience on earth today as a result of our inactivity. Thus the overall amount of non-consensual suffering taking place on earth right now would have been duplicated; suffering caused by twice as many animals ripping off each other’s flesh to survive per brute instincts. This is one (of many) reasons as to why Unconditional Extinctionism lacks coherence when it targets human beings in the present.

Indeed, Natalists don’t promote procreation in order to abate suffering in the wilderness, just as ordinary breeders don’t ordinarily breed with those same goals in mind. Their collective intentions have nothing to do with safeguarding animal welfare by facilitating hastened depopulation of non-human species. Nevertheless, their collective efforts have amounted to a gigantic plus from where things currently stand. This remains so even after we counter in all the harm that carnists continue causing to select remaining species via factory farming. Such a human-friendly tally is deeply unintuitive, but the plummeting wildlife numbers unmistakably point to human presence serving a valuable end on a panoramic level, albeit inadvertently.

I'm not sure what to think.

One could counter Rhys' argument that building roads, expanding human civilization, etc., and all the animal death and suffering it entails does reduce net suffering in the long run by AntiBullShitMan's logic. Meanwhile, raising livestock, whether "humanely" or not, can never reduce net suffering because it brings being into existence and inflicts pain on them. Expanding our civilization kills and inflicts pain, but every killed animal is incapable of reproducing, so on strictly utilitarian grounds, while its death might be unpleasant, we are preventing possibly tens of thousands of progeny from ever being born and ever suffering. No similar argument can be made w.r.t. to livestock, because we are responsible for their population (and existence). But if we accept that veganism is necessary because suffering-reduction is necessary, and the harms that are consequences of veganism reduce net suffering, wouldn't this obligate us to kill as many animals and humans as possible? I don't know.

It seems that some arguments for suffering reduction should necessitate suicide, since merely by living we inflict harm on others, and calling any harm but inevitable harm (as in, the laws of physics necessitate it) "necessary" is arbitrary. This essay is the most in-depth study I know of on the suffering-reduction potential of suicide. It concludes that we ought not kill ourselves because the pain inflicted on grieving family members outweighs all the harm we inflict on people, including harm on animals and sweat shop labourers.

I'm not well-versed in rights theory (or ethics in general, really), but can we resolve the rights conundrum that Rhys raises (that it's "odd" to give animals rights when they don't have the capacity to respect our rights or cooperate with us, but we have the capacity to respect theirs, therefore forcing us to cede to them in every decision) by only giving rights to animals that they can reciprocate? I argue that one such right exists: the right to not be brought into existence. We must say that animals don't have a right to life (since bears would gladly kill us), which would make hunting permissible, but we can argue for antinatalism on deontological grounds, saying that all sentient beings have a right not to be brought into existence (if you say it's meaningless to talk about non-existent beings, this essay argues otherwise; I apologize if the wording of this claim is "messy"). Then we'd have a moral obligation to avoid supporting anything that involves raising livestock. It would not be contradictory to kill animals while farming in this framework, since we are merely required never to bring them into existence. Since animals cannot bring us into existence (by farming us), the right is easily reciprocated -- we need only become antinatalists ourselves. This necessitates de facto veganism, since many people find hunting impractical.

I ultimately agree with Rhys that veganism is neither necessary nor sufficient. But it's certainly preferable, and it's not very difficult.