If you say, Birth on US soil = Natural born citizen, then two terrorists could come here give birth to a child and that child could grow up to be President. That is wrong.
The child would be a citizen, but not a “natural born” citizen because the parents were not citizens at the time of his birth.
Now if two persons come here and become citizens, then give birth to a child, then that child can grow up to be President because the child would be a “natural born” citizen.
As terrorists they would technically be 'hostile occupying aliens', or at least I would consider them so. There are other excluded classes. I won't argue for the right of a terrorist's children to be eligible for POTUS, or even a citizen. I have previously mentioned thet La Raza would count as a hostile occupying army and that hteir children are not POTUS eligible. I know how ridiculously difficult to win such a case would be as well. Location of birth is critical. Status of parents as diplomats, Indians, or invaders is critical. Citizenship of parents is not.
Why is it wrong? It is a fundamentally American concept that we do not punish children for the actions of their parents, at least not by law. Legally-speaking, the motivations and behavior's of a kid's parents make no difference when it comes to whether that kid can run for President someday.