Lots of articles about this. Not one expert agrees with you, not even on the left.
Cruz would be the first President born outside the US. He would also be the first President to have dual citizenship. Cruz was a Canadian citizen at birth thru birthright citizenship. His mother had to register his birth at the consulate to convey citizenship. So Cruz was a Canadian citizen before he became an American citizen.
Should the children of illegal aliens, tourists in the US, or those holding green cards who elect not be citizens be eligible for the Presidency?