Can a company not hire you because you are a man?

As a general matter, no--refusing to hire someone because he is a man is illegal sexual discrimination, and you could potentially sue the employer. That said, there are limited occasions when it could be allowed. A classic example is, a company could refuse to hire a man as a women's room or woman's locker room attendant. In the case of nurses, I'd imagine if the specific position you were interviewing for required a woman for some legitimate reason, what they did might be legal, but not otherwise. From what you write, it would be worthwhile to consult with an employment law attorney to discuss this matter in detail--you may have a cause of action.