<nitpick>I think the word you're looking for is pet -- the standard meaning of domesticated also includes livestock, whose meat, if anything, I guess is seen as less ethically problematic than game by many people. (From your username, I'm guessing you're not a native speaker. FWIW, neither am I.)</nitpick>

You're right, it's not exactly a matter of domestication, but it's not only pets, either; horses fall into that category just as well. As I said, it's too fuzzy and arbitrary.

You know, you could decide not to eat certain kinds of meat for reasons other than “taboo”; for example, that it's too expensive (either in terms of money or of energy) or that you don't like the way it tastes or for signalling reasons or for health reasons or because you'd be uncomfortable with the idea of eating it for purely emotional reasons or whatever. Just because oysters don't feel pain doesn't mean I'm obligated to eat them, if I know better ways to spend my money or if I prefer the taste of different food.

But that's exactly the point, I was deliberately looking to find some general system that would allow me to classify food into two categories. Of course I don't eat something I don't like or that's otherwise undesirable if it can be avoided, that's not the issue here. This is purely about the moral part, and the problem is that there's some meat I have moral obejctions to eating, and other meat I don't, and there's a very slippery slope in between. If I object to eating human meat, where's the watershed? How about the homo sapiens species in general, such as the extinct subspecies h. sapiens idaltu? How about other species of the homo genus? Apes? Monkeys? Aliens?

A collection of ad-hoc rules isn't a system of ethics.