People also say that Batman is not a superhero because anyone can do what he does if they had the resources. Guess what? If you are a genius, are in prime physical condition, and fight crime: congratulations... you are a superhero.
Batman is also a superhero because he fights super villains in addition to petty thugs. The super villains have powers such as superhuman strength (Bane, Killer Croc), the ability to fly (Man-Bat, Killer Moth), the ability to control plant life (Poison Ivy), et cetera, et cetera. It takes a superhero to defeat a super villain or else the police would be able to take care of these guys and we wouldn’t need Batman. If Batman wasn’t a superhero, and just “an average guy” then why does the police call on him to help them out?