Ponyboy and Cherry are able to tell each other things that they cannot tell other people because they come from different social groups. They do not feel comfortable saying these things in front of members of their own groups because they feel judged and think that members of their group will not accept them. Ponyboy says about Cherry, "She was coming through to me all right, probably because I was a greaser, and younger; she didn't have to keep her guard up with me." Cherry tells Ponyboy that the socs have to feel detached from everything to seem sophisticated, and she has to feign this kind of detached attitude with her friends. She feels the greasers can be more emotional. However, Ponyboy will not judge her if she voices her true feelings, and she does not have to keep up appearances with him. He is also younger than her, so she feels that she does not have to impress him. Ponyboy is similarly able to speak honestly to Cherry for the same main reason—he thinks that she will not judge him.
Of course, we cannot know for sure why Pony and Cherry tell each other these things. But my feeling is it is because they are not really part of the same social circle. They can tell each other "secrets" and assume that the other person will never tell anyone who matters.
Cherry, for example, will also not have to worry about hanging out with Pony and having Pony know her secrets. It's like a one time thing -- they're meeting, talking, but not having to deal with how things will be in a long term relationship. Pony won't have to worry about what Cherry thinks of him now that she knows this stuff -- they'll essentially never interact again.