You are conflating a child with the parents again. False equivalence fallacy.
That is what you do. It is the source of all of your errors on this matter. You won't get it right until you learn that the child is not the parents. Yes, you have already griped about how difficult it is for you to grasp this, but you need to keep working at it until you get it right. Until you do, you will be unequivocally in error.
Any child born in the United States is a subject of jurisdiction that matches the mother.
You just pulled that out of your ass; that's why it stinks as it does. The 14th Amendment is clear that the parents, who are not the child, do not factor into the equation. All of those references that you imagined you saw regarding the parents of persons born in the United States were just that, i.e. imagined. The 14th Amendment does not mention the parents of persons born in the US because they, and their status, are irrelevant.
Illegal aliens are not subjects of US jurisdiction.
Illegal aliens are completely subject to US jurisdiction when they are in the US. Watch a deportation. Watch an illegal being handed a sentence or a judgement in court. Your claims are absurd.
Rights do not come from a piece of paper.
Correct. The inalienable right of US citizenship by birth precedes the Constitution.
Children born in the United States have the same jurisdiction as the mother.
The mothers of children born in the US are completely irrelevant. Children born in the US are US citizens, irrespective of the status of the parents and irrespective of anyone who makes up booooolsch't about the relevance of mothers' statuses.
Rights do not come from a piece of paper.
Correct. The inalienable right of US citizenship by birth precedes the Constitution.
There is no inalienable right of US citizenship.
The right of US citizenship by birth is inalienable and precedes the Constitution.