The "do not kill animals to eat them" argument is for vegetarianism, not only veganism.
I understand and see the consistency in the argument for vegetarianism: "I'd rather not kill animals to eat them". As an omnivore myself, I think that all omnivores should at least occasionally participate in the slaughter and processing of the meat that they eat, in order to make a fully informed decision about whether causing an animal to die is worth it to them for the flavor and nutrition offered by meat compared to its alternatives. Old-fashioned though it is, I think that if you wouldn't kill a creature yourself, you have no business eating it.
The argument for veganism beyond vegetarianism, however, strikes me as incoherent when its claims are taken at face value. Veganism at its extreme purports that no product in whose production any animal could have suffered is acceptable for anyone to consume.
This falls apart in 2 places for me:
First, most vegans will happily consume products which required the labor of animals, and whose production harms animals, as long as those products aren't on their list of taboo items. Vegans categorically reject eggs even from spoiled pet chickens who get better nutrition and medical care than many humans in developing nations, because eggs are on the taboo list, and yet instead of eggs they'll recommend substituting plant based products grown in industrial monocultures whose planting and harvest endangers entire species of birds. Vegans categorically reject honey because they claim to care about the wellbeing of bees, and yet they encourage consumption of products whose production requires shipping hundreds of thousands of bees to a central location. This puts great stress on the hives, and exposes them to all kinds of diseases like the first day of kindergarten, compared to leaving them alone and harvesting a frame or two of honey every so often when they make more than they need.
Second, the vegan rhetoric of "don't eat these taboo items because animals suffer to make them" appears inconsistent to me because I regard humans as being animals too. I think that if you want to minimize the amount of suffering that goes into your diet, it's essential to consider the experiences of the humans who farm the products that you eat. "The vegans" as a cultural force tend to diatribe ad nauseum about how ever harvesting any honey hurts the bees, or ever harvesting any wool hurts the sheep, yet I do not see them showing comparable vitriol about the impact of poor labor practices on the suffering of the humans whose labor produces cheap "vegan" foods. The wool and honey stuff makes me especially suspicious about the claimants' experience with the actual products: I have kept pet sheep and seen how happy they look to get out from under their heavy wool coats in the warmth of early summer, and how calmly they tolerate shearing when a skillful professional denudes them. I have worked with beekeepers enough to see how carefully harvesting a frame of honey avoids injury to even a single insect, and seen how in wild hives, they will fill every bit of space with honey until they're forced to swarm because there is inadequate space left for the colony to grow.