What is Ponyboy’s issue with Johnny’s suggestion that they disguise themselves?

Ponyboy doesn't want to cut his hair.... his long hair is a part of his identity.

It was my pride. It was long and silky, just like Soda's, only a little redder. Our hair was tuff--- we didn't have to use much grease on it. Our hair labeled us greasers, too--- it was our trademark. The one thing we were proud of. Maybe we couldn't have Corvairs or madras shirts, but we could have hair.