I think Scout is noticing how emotional Jem is right now. He has two reasons to be as emotional as he is. First of all, he has just seen a major injustice and is old enough to grasp the horror of how terrible men can be to other human beings. Secondly, Jem has just hit puberty and the changes his body goes through are completely messing with him. We have seen him as a highly emotional character throughout, but this is the first moment a little sister calls him on it.
I don't think Jem was outright acting like a girl, but Scout's sentiment likely meant emotional and that rings true with Jem. His emotion is not only okay with me, I praise his character for it. Jem is the one redeeming character in this book that should give all of us hope for future generations. Because he cares when a living thing gets hurts, tomorrow could have less hate.
Jem and Scout seemed to do just about everything together in Part One of To Kill a Mockingbird. Scout comments that Jem seemed happy to have her as company during his many hours of reading to Mrs. Dubose. But at the beginning of Part Two, things have changed. Jem no longer seems to have time for his sister and tells her repeatedly to "stop pestering her." Thinking Jem may have "a tapeworm," she seeks out Atticus' advice. Her father told her that Jem "was growing," and that she must be patient with him.
Jem is going through the first stages of puberty, and his moodiness and inconsistencies are just some of the early signs of his new growth.
I think that the part you are talking about here is in Chapter 25. In that episode, Jem and Scout are sitting on the porch. Scout wants to smash a bug. Jem does not want her to and tells her not to. He says that the bug never did anything to her.
I guess whether you agree or not depends on what you think girls should act like. Jem, to me, is feeling bad about what happened to Tom Robinson and does not want anything else that is innocent to get killed. You can decide for yourself if that counts as "acting like a girl" in your own mind.