Yeah choosing to abstain from eating certain animals for moral reasons (dogs/cats/cows/horses) and not others (pigs/chickens/fish) is definitely weird. Though the majority of people in western society fall into this category, you just moved one more animal across the boundary due to normalization. If you were brought up with pigs, chickens, and fish you'd probably abstain from those too.
The real question to ask though is despite normalization, what's actually the right thing to do? Is it actually okay that some people eat dogs, cats, and cows? Or is it wrong to do this?
People should put more effort into reconciling this dissonance, because slaughter and oppression is not a matter we should leave up to the normalization of society to decide. Society has countless times normalized immoral things.