In "The Outsiders", why does Pony have a problem with Johnny's idea to disguise themselves?

In chapter 5 of "The Outsiders" Johnny and Ponyboy are on the run from the police because Johnny killed a Soc while trying to protect Ponyboy.  Johnny decides they need a disguise.  He buys peroxide and tells Ponyboy he must cut his hair and dye it blonde.  Ponyboy has a big problem with this.  He tells Johnny he doesn't want to cut his hair because it took him a long time to grow it just the way he wanted it.  He is very proud of his long hair and he doesn't want to change it in any way.  He finally agrees and Johnny cuts Ponyboys hair with a knife, then Ponyboy cuts Johnny's hair.