I see. There are no laws to that effect, and no one but you says so, but that is your opinion.
I am glad your opinion doesn't matter any more than my opinion. For that we are both lucky.
The children of bank robbers don't get to keep the money their parents stole, even if they have become accustomed to a high standard of living. Illegal aliens steal presence in the USA. Their children shouldn't be allowed to keep what their parents stole, either. We don't cut lawbreakers slack and let them continue to commit crimes just because they have children, and we don't cut the children of criminals slack just because they like what the parents stole.
Those children have the bad luck of being born to criminals - we take care of those children and foster them out, if need be. We don't want them begging or prostituting themselves in the street because we are a decent, compassionate society. But we don't owe them a living, either, or an education beyond k-12. Same goes for the children of illegal aliens - we don't owe them a living, nor do we owe them a path to citizenship. They are legally citizens of a foreign country. Their parents stole them a place here - they didn't come by it honestly.
The parents should take their US born children back to their home country to raise them, where they would have been raised had those parents not chosen to commit their crime of illegal entry. If we still have 'birthright' citizenship for children of foreigners by the time those children become of age, then those children can apply to be repatriated at the proper time. Their illegal children should all be returned to their countries of origin with their parents.
There is nothing wrong with our immigration system. What's wrong are people who spit on our laws and come here illegally just because they want to.