Moral Axiom - Life is good; on average, it is better to be born than not born; the pros generally outweigh the cons. Metaphysically pro-life.
Moral Standard - Moral conclusions cannot violate moral axioms.
P1) Causing suffering is bad
P2) Eating meat causes suffering
C1) Don't eat meat
P1) Causing suffering is bad
P3) Birth causes suffering
C2) Don't give birth
C2 violates moral axiom, and is hence morally false.
If C2 is false, at least one premise must be false, among P1 and P3.
P3 is a true description of reality.
C2's error is derived from P1.
If P1 is in error, all conclusions derived from P1 are in error.
C1 is derived from P1 and therefore C1 is in error.
It is erroneous to conclude "don't eat meat"
The problem is that vegan logic often operates deontologically instead of consequentially. When you say "causing suffering is always bad, even if the attending joy outweighs the suffering" you have committed yourself to a philosophy that leads to anti-natalism - because to be born is to enter a world where suffering is inevitable, and birth is directly causing the suffering that will follow.
When vegans say that farms should not raise animals, they are concluding that "it is better for these farm animals to have never been born". Veganism is hence an anti-life philosophy. Once you conclude that it is better for animals to have never been born, then it is easy to apply this same moral conclusion to humans.
Deontology is stubborn. It says that something is always unacceptable, no matter what - regardless of any benefits that might outweigh the costs. When you drop the deontology, you can say "in general the benefits of life exceed the costs in terms of suffering, and hence it is better to have been born". This allows more philosophic flexibility to allow for farming and allow animal slaughter, but simultaneously promote the minimization of the suffering and maximization of the joy of the animals along the way. This allows for the promotion of humane environments for animals and near-painless executions, while not fully banning the birth of these animals in the first place. By having a more flexible utilitarian philosophy, one has the philosophic tools to avoid the trap of anti-natalism which is an anti-life philosophy. The anti-natalist is usually so disgusted by the inevitability of human suffering that they would rather not exist than endure it. They find it immoral to "throw" humans into existence against their will and without their consent. If the anti-natalists could have their way, it would be illegal to have children, and in one generation humanity would cease to exist.
But deep within most people is the instinct that life is good, sentience is beautiful, and enduring suffering is noble. These instincts are only natural given that evolution naturally wants to promote life. Those with anti-life instincts will Darwinistically disappear from existence, and only those that are metaphysically pro-life will persist. Essentially, anti-natalism is fighting a battle against evolution that it can't win. The objective facts of reality are guiding us towards a metaphysically pro-life philosophy. As Friedrich Nietzsche would say, the correct thing to do is to say 'yes' to life!
The thing about the state of life is - death is inevitable. So you can analyze different types of death. How bad is death to a wolf? Death by slitting the throat? Death to a hunter's bullet? Death by starvation over a long period of time. Or the most idyllic death - death by getting old, getting tired, breaking bones, collapsing, going blind and deaf, losing your memory, and slowly dying from lots of discomfort spread over a long period of time.
Which is better - a quick and highly painful death, or a slow and minorly painful death? It isn't obvious that a quick and highly painful death is worse than a long drawn out process. So technically, all of the types of death are pretty bad. If slitting a throat is so bad, then letting them suffer in discomfort until their eventual natural death is also bad. Hence, viewing death as unacceptable leads to the conclusion that birth is unacceptable. The same thing applies to suffering since suffering is almost as unavoidable as death.
Sure, some life conditions are so horrible that death (or never being born) is preferable, since the experience of the creature is net-negative on whole. But if we acknowledge that on average, life is a net-positive experience and hence a morally acceptable fact, then we can build a metaphysically pro-life philosophy upon that foundation.
A nuanced take on veganism could be termed "threshold veganism". "Threshold veganism" implies that it is only bad to abuse animals when a certain threshold of suffering is meted out. This would be a utilitarian approach to veganism that doesn't fall into the pitfalls of deontology. A certain threshold might be "suffering becomes greater than happiness". Once an animal's life is more miserable than happy, it is no longer ethical to take advantage of them as a resource. But if the suffering of the animals is able to be reduced below the threshold, it may be ethical to farm them.
It seems logical to think that "threshold veganism" would lead to "threshold antinatalism". Perhaps if the state of a society is such that most people suffer more than they are happy, a threshold has been met, and it would be unethical to bring children into the world when you know that all the society has to offer them is net-suffering. This means that during bad conditions, the threshold antinatalist will be anti-birth, but when conditions become better for life, the antinatalism "turns off" and they are okay with birthing people into the world at that point.