In The Outsiders, what does Ponyboy mean when he says that it is not good to be a greaser and be sensitive at the same time? It's in Chapter 6, page 88.
This reference comes in Chapter Six as you have identified, when Dally comes to see Johnny and Ponyboy in hiding. Ponyboy is commenting to himself on the differences between Dally and Johnny, after Johnny has just insisted on asking if his parents have asked after him at all. Although the gang had tried to make it up to Johnny and be substitute parents, it is clear that it is impossible for anyone, no matter how caring, to take the place of parents. As Ponyboy compares Dally and Johnny, he says:
No wonder Johnny was hurt because his parents didn't want him. Dally could take it--Dally was of the breed that could take anything, because he was hard and tough, and when he wasn't he could turn hard and tough. Johnny was a good fighter and could play it cool, but he was sensitive and that isn't a good way to be when you're a greaser.
Ponyboy therefore establishes that to be a "good" greaser you need to be able to toughen yourself internally, not just physically, but emotionally. Johnny, although he is able to "play it cool," remains internally vulnerable because of his sensitivity. This is not a good quality for a greaser to have given the nature of their lives as explored in this excellent novel.