Some arguments are pretty spectacularly wrong. One such argument in favor of the existence of god is Pascal's Wager. There are so many ways to decisively rebut this argument, it can be hard to know where to start. It's such a fallacious argument that even if many of its controversial elements are accepted, it could be slightly modified to be an argument for atheism. It fails to be convincing on pretty much every level on analysis.
Some conclusions, by contrast, work the other way. Even if you jettison many of the strongest features of the arguments in favor of a given conclusion, you may still reach the same (or a similar) result. There are just so many individually persuasive reasons to believe that it is hard to see how belief in the conclusion is plausibly denied.
One such conclusion is that veganism is morally required. To be clear, veganism is the practice of avoiding the exploitation of non-human animals for food, clothing, etc. Personally, I think there is good reason to accept a strong animal rights, abolitionist view, which rejects the species distinction as morally relevant. I also think that many of the qualities that are thought to draw out important differences between animals and humans are largely irrelevant with respect to what rights one has. However, even if you reject the controversial elements of my views, the rest of your moral beliefs regarding animals still rationally require a form of veganism.
For example, some people reject "rights" in general as a legitimate moral category, most notably utilitarians. But within the utilitarian tradition, there is a strong history of recognizing animal welfare as comparably important to human welfare. Often, human welfare is given higher priority, supposedly because we have a higher capacity for pleasure. I find this assumption totally unfounded; just because we might prefer pleasures that an animal cannot experience (like the pleasure of reading a philosophical text), that doesn't mean that the "lower pleasures" of animals are less valuable for them. This is obviously a speciesist assumption, and in fairness we should be agnostic about whether or not some species have higher or lower capacities for pleasure.
Regardless, if we take this non-rights utilitarian approach, we should still be vegan, because of the immense suffering that is perpetuated in animal agriculture. Many utilitarians argue as much (Peter Singer, for example, though I should add the caveat that he thinks veganism is a more flexible requirement than I do). Even if you disagree with my take on the capacities of human and animals for pleasure, it's clear that there is great suffering involved in animal agriculture, so this disagreement has a negligible effect on the force of the argument.
Singer also believes that the painless death of an animal is not bad in the way it is for a human. I'll be posting on this topic in the future, but it suffices for now to say that I think he's absolutely wrong. Nevertheless, as before, even if you take the weaker claim in defense of animals, that their painless deaths are not wrong, one still cannot justify participating in the stupendously painful lives that animals live. Even if we imagine that their lives aren't nearly as terrible as most of them certainly are, there is still more pain involved in exploiting these animals than in helping them live happy lives, and very little that we get out of their suffering. Given that many vegans appear to live happy and healthy lives, whatever preference one currently has cannot justify the ongoing costs to animals that such preferences cause.
Suppose instead that you don't buy into utilitarianism. Perhaps you accept something more like a common sense morality, and you think a speciesist bias is acceptable. You might not think that "rights" makes much sense when applied to animals. Still, most people think animals command some moral consideration. At the very least, we shouldn't impose unnecessary suffering and death on creatures if it can be avoided without much cost. But what is being non-vegan than the imposition of suffering of death on animals? The production of meat, dairy, eggs, and other animal products is torturous for those animals. And as any vegan will tell you, this exploitation is certainly not necessary by any stretch of the imagination. Gary Francione argues very persuasively along exactly these lines.
Even if you reject anti-speciesism arguments, arguments in favor of rights, arguments about the commensurable nature of human and animal pleasures, arguments about the badness of animal death, you still accept that unnecessary suffering of animals is wrong. And most of what veganism amounts to is the avoidance unnecessary use and suffering of animals.
Perhaps some people think animals aren't morally relevant at all. Descartes purported to believe as much, but few today defend such a view. I find such a view to be so implausible that I feel no need to argue against it.
I think the views I have about the moral status of animals to be correct. These views are extremely controversial and unpopular, but it's also true that there have been times when other true moral beliefs have been controversial and unpopular. In fact, I think it's prima facie more plausible than not that our current society is seriously mistaken about some moral matters of great importance. But my belief in the necessity of veganism is even more strongly supported than my beliefs about the moral status of animals, as I have just tried to show.
It's also the case that most vegans I know have similar views about the moral status of animals as I do, even though as I've argued, one does not need to accept these views to see veganism as required. This further fact suggests, though not definitively, that our current practices of animal exploitation bias us towards speciesist views.
So you might think I'm crazy for arguing against speciesism. I think that there can be no rational basis for a bias in favor of the human species qua species, and I think there are exceptionally good reasons for according fundamental rights to all sentient animals. But even if I'm crazy, you should still be vegan.