Why would being born in the country give you citizenship or the right to stay? The citizenship is inherited by blood in large majority of cases in the world, the child has the nationality of the parents, not just the country where you "give birth", if I stay in Thailand with my wife and she suddenly give birth there, you expect the child to be Thai even if both parents are European? :/
Deporting parents (thus with their children) is normal if they are staying in the country illegally without any sort of valid visa or permit, what's the alternative? Give citizenship to anyone crossing the border?
Yes, this the gist of this proposal by the ethno-nationalist right. That is what it says in the linked article above, did you read it? If you did, why do you ask more? If not, how is it that you care enough to ask?
Deporting parents (thus with their children) is normal if they are staying in the country illegally without any sort of valid visa or permit, what's the alternative? Give citizenship to anyone crossing the border?