In "The Outsiders", why doesn't Ponyboy like referring to Sodapop as a dropout?

In both chapter one and two of The Outsiders, we find that Pony hates the thoughts of Soda as a dropout. Soda has always been the one who protected and watched out for Pony, so when he drops out of school, Pony is left on his own. When Pony, Johnny, and Dally are at the drive-in, Cherry asks Pony what grade Soda is in. Pony hates it when he has to tell people that his brother is a drop-out.

I winced inside. I've told you that I can't stand it that Soda dropped out. "He's a dropout," I said roughly. "Dropout" made me think of some poor dumb-looking hoodlum wandering the streets breaking out street lights--it didn't fit my happy-go-lucky brother at all. It fitted Dally perfectly, but you could hardly say it about Soda.

Ponyboy Curtis is one of the most interesting characters. He is a member of the greasers, yet he is a quite sensitive young man. He is very smart. Pony is stuck in a situation that looks bleak, yet his future could be so bright. He has high expectations of his brother, and it really bothers him that Soda dropped out of school.