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.
You are still trying to remove the child's birthright because of actions not his own.