The simpler, logically consistent solution would be that the child’s citizenship is only granted if the parents are citizens. (Or at least if parents are not illegal immigrants). Then when you deport the parents, you can legally deport the child too. It still is not a pleasant situation, there is no ideal solution here, except he should have never been let in at all, but once he is, these seem the only choices
Citizenship by blood creates its own problems. I am eligible for Polish citizenship if I choose to pursue it based on where my ancestors lived. I have never been to Poland, don't speak the language, and don't really know that much about the culture or feel any loyalty or even much affinity to Poland. On the other hand, let's say that someone is born in Poland to immigrant parents. Culturally they are entirely Polish - they lived their whole life there, speak the language, were educated by the Polish school system and consider themselves entirely Polish - they've never lived anywhere else. Yet they would not have the same ability to become a citizen that I have. If I got Polish citizenship, I'd just take whatever benefits I could from it and contribute nothing to Poland. How is it logical that I could be a Polish citizen and this person couldn't be?