That is assuming he was born outside the country. If he was born in the US, his birth here and his mother's American citizenship could have made him a citizen at birth.
I'm not sure of the details any more. It's all very fuzzy to me at this point, but if you want to make a strong case against "anchor babies" somebody who had an American mother wouldn't be the best place to start.
You state: If he was born in the US, his birth here and his mother’s American citizenship could have made him a citizen at birth.
A Citizen yes, but it wouldn’t make him a natural born Citizen which Article 2 Section 1 calls for to be president.