Why is this about "the west"? Also what is a vegan who objects to eating dogs? Also what's morally wrong with loving a meat animal like a pet until it's time to slaughter it? We love all kinds of things that we know we'll eventually get rid of - is that really wrong? So many questions.
If I picked up cats at shelters, fed them, cared for them, with lots of space and toys, and then after a few months slaughtered and ate them, that would be the most ethical meat consumption right? It would certainly be better for the bird population than letting them go to homes that allow them to roam.
So why does it feel wrong to pick up a healthy young animal that trusts you and slit its throat?
I hope you are aware that more than 99% of all animals raised for meat have a very different experience to what I describe, and not in a good way. So even if the slaughter is not an issue, consider their life.
I definitely get it; there's a lot more separation between the average person and cows than there is with dogs. Many people keep dogs as pets, but few interact closely with cows. That definitely makes it easier to dismiss their killing.
I think expecting moral consistency from humans is a bit of a high bar, as we're well known to be irrational and emotional creatures. It's probably better to appeal to people's emotional side if you want to change their views, for example by taking them to meet cows in a farm and showing them how they're sentient creatures too.
Sure, we are irrational and emotional, but the whole idea of modern society is that we surpass those base level instincts into rationality and consistency. Consistency is still important and something that should be focused on