The problem isn't that we pet birds, it's that we eat them. Or more specifically we gather them in huge, unsanitary populations in close contact with humans as they are raised and slaughtered.
This reminds me of how people think AIDS spread from other primates through bestiality, when bushmeat was the correct answer. I guess it's easier to imagine bestiality than the consequences of carnism.
*not vegan, Just finding it harder and harder to dismiss them.