A human being eating/ killing a chicken is not the same as a human being eating/ killing another human being because of what makes us different from a chicken, empathy. Since human beings are the only animals capable of this, they are able to reciprocate morality for each other, treat someone the way you want to be treated or at least don't treat someone in a way that causes suffering. I may be able to do this for an animal, but an animal is incapable of reciprocating. Like it or not, in a purely objective sense, the lives of human beings are more valuable than the lives of other animals because human beings are capable of morality, other animals are not. You are arguing that morality is not universal, but the only morality is that which is universal. Like you said, some cultures may believe that eating other animals is wrong or even that eating certain plants is wrong (Jainism), however ALL of those cultures would agree that killing a human being is wrong, that makes this universal. I believe what you are calling your moral code are your values (not saying there is anything wrong with living according to your values), true morality is always universal.