I actually think it is preferable NOT to eat animals, and I would transition to grown meat if it was available. I eat them because it is culturally acceptable and I grew up doing it, although I am not comfortable with the morality of it. If I had grown up in a culture that ate people, like many existed throughout history, I'd probably be eating people too. And I'd be talking about how we probably should avoid eating people.
The question is, what makes human suffering unacceptable if suffering of other animals isn't? I think the death of a human is far more significant than the death of an animal, given our natural affinity of humans, and the social network humans have, which means the death of a human will cause the suffering of other humans connected to the deceased. I also do think human individuals carry more value given some definitions of value that I identify with (richness of human experience and knowledge for example). But even given the value argument, and even if we agree that human suffering has more value, surely if it has any value at all, then so must the suffering of other animals. I don't see how it can logically be another way.