Animal Rights?

I love animals. I don't really eat them anymore. In fact I was a quasi-borderline vegan that I vaguely ate any dairy products let alone meat.

But now I live in France...

So now  I consider myself a vegetarian who adapts. What can I say the meat and dairy quality is far from dubious as it is in the USA. Thus I am not that scared to eat it on that principle.

But why should I care about animal rights? I am trying to postulate philosophical  reasons why eating animal flesh is wrong. I do get grossed out from time to time. When I do eat meat, I really try not to think about flesh and blood and ugh. But it is getting very hard for me. The very idea of eating meat is very bizarre to me now.
But what rights to animals have? I just can't grasp this concept.