Of course it's not saying that any other nationality is substandard to that of the US (note I didn't say anything about Mexicans!)
You are punishing the child in the sense that you are tarring it with the brush of being a criminal before it has even had the chance to breathe. Furthermore, by not allowing the child citizenship, you are denying the child things like healthcare or education (both of which I appreciate some of you do not class as human rights). It's the child that is more likely to die because their parents are scared of being reported and deported when turning up at a hospital; the child who is going to grow up without an education and end up flipping burgers for a cash in hand, no questions asked wage.
Maybe we have different morals, or different opinions on issues like this (and that's fine.. we are, after all, from different sides of the pond), but I'm strongly of the belief that children should be given the best opportunity in life, regardless of whatever mistakes their parents have made. If granting them citizenship will help that, then I really don't see a problem.