The reason it’s not clear to me, is that he is a citizen by birth through his mother. He never had to go through the naturalization process, because he was a citizen by birth through his mother. Because of legal standards such as this, that’s why it’s unclear to me whether Ted Cruz can run for president.
To my knowledge, courts have never ruled on exactly what natural born citizen with reference to presidential eligibility means. Which is also why it’s unclear to me, even though apparently very clear to you.
There are two categories of citizen:
1. Naturalized citizens, who acquire citizenship by act of government.For a court to find that someone who is a citizen but was not expressly naturalized to be other than a native-born citizen would require the creation of a third category, which would be a breathtaking act of judicial activism even by modern standards.
2. Native-born citizens, who hold citizenship by birthright.