Taking this extremely simplistic argument to its logical conclusion, then you would say that if it's okay to eat a chicken it's okay to eat a human being. Both are animals, after all.
Well in some cultures it actually is ok to eat humans. Not many, admittedly, but the problem with trying to insist upon moral absolutes is that there will always be examples to prove you wrong.
However, our minds are supposed to be capable of making distinctions—and yes, a dog is a superior being to a chicken. And not just because our culture says so.
This is a nonsense. There is nothing that distinguishes a dog from all other animals except your cultural conditioning leading you to see them as different.
What's so wrong with accepting that it's cultural anyway? You still have the right not to eat dogs yourself. Why don't you want to recognise that human perceptions of animals aren't innate truths, but things we have learned from the culture we grow up in?