then a child born of illegal Mexican immigrants would be citizen of nowhere.
So? That's their problem, and it's a direct consequence of their actions in leaving their country illegally.
The child didn't do anything illegal, and in this country we do not visit the sins of the parents on the sons. That's not a good solution.
First off, this whole question is based on a hypothetical - what if Mexico denied citizenship to children born of Mexican parents outside of Mexico. I don't think there's any nation on earth that would ever do that, so it's a moot point.
Either way, the child isn't being punished, but simply not being rewarded. There's a difference.
We are not punishing the child, we are just not giving them anything to which they are not entitled. You are using the same logic that the people who support the DREAM Act are using. They try to claim that by denying a child who was brought here illegally as a minor a subsidized college education we are punishing the child for the illegal acts of his parents. It is not a punishment to deny him a subsidized education because a subsidized education was never a right. Likewise, it is not a punishment to deny a child of illegals, citizenship because it is not that child's right. Only ONE of TWO conditions for birthright citizenship have been met.