Can I sue a company for not hiring men?

You can but you will need to PROVE that they didn't hire you based on your sex. That's a tough one. They have the upper hand by stating that a female was more qualified than you...whether or not it is true. But if Target, Walmart, fast food places won't hire you either, you must be screwing up the interview somewhere. because those places hire anyone. Find out what you're doing wrong.