If a man is a citizen of the United States, then he was

born in the United States. Sam was not born in the
United States. Therefore Sam isn’t a citizen of the
United States?

2 answers

Not necessarily. There are other ways to become a citizen, or to be born a citizen. The first ststement is not correct; no fact can be deduced from false statement.

Other ways to be be a citizen without being born here:
(1) become naturalized
(2) be the child of at least one American citizen parent, although born outside the country.
(3) Be born in Puerto Rico or Guam
Drwls is, of course, correct in the various ways of becoming a citizen.

I interpret your question differently. Your initial statement is wrong. However, if it were correct, then your argument would be true.