It's difficult to describe gender dysmorphia without pointing to behaviors, but this conflates two very different things. Certainly no behaviors are strictly female or male, and the use of behaviors like playing with dolls or enjoying makeup are problematic and set off red flags for anyone who is gender conscious. But if someone of cis-gender has to describe why they felt comfortable in their gender, what would they say? It would be easy to point to gender conforming behaviors. I've heard many people say something along the lines of, "I like being a girl/boy", which I think translates into "I like doing the behaviors that a girl/boy does". I don't think, and maybe I am completely wrong, that it usually means that the person has a deep sense of comfort with the physical space they inhabit. So identity and behavior are often conflated in our society. Judith Butler has taken this idea to its extreme in saying that behavior creates gender.
If behavior entirely creates gender, then it is difficult to see how a trans person could exist. If all I were given was male behaviors, then how did I form the idea that it was not for me. By saying that I'm trans, is this simply saying that I don't like to do typically male activities? For me,being trans cannot be explained or justified with behaviors. While many of the things I like would fall into the girl camp (makeup springs to mind), there are quite a few activities that I also enjoy (weightlifting, mechanics) that are over on the stereotypical male side. And I agree that associating any behavior with a gender is deeply problematic.
I did not decide to come out as trans and begin transitioning because I wanted to do more female typical things like wear make-up. I could have done these activities within the context of a male presentation, and most of the people I know who cross-dress or engage in gender bending have no desire to change their biological sex. So what did I want? I can say that in my own experience being in a male body has been deeply unpleasant. Simply being present in it, especially since puberty, has been an unrelenting source of unhappiness. Every trans person has a different experience of their body, so I can't say what it is like for them, but body dysmorphia is a common aspect of the trans experience. I don't know what causes the dysmorphia, or the neurology behind it (no one does at this point), but I do know that when I say I am trans I am not talking about the behaviors.
The behaviors, however, make more sense and are easier to explain than this deep existential feeling of being in the wrong body. It's easy to conflate the two in conversation, but by parsing out the internal feeling of identity from the behaviors we should seek clarity and not a way to devalue that internal experience. I admit that I don't understand this very well. The roots of a person's identity tap into the deepest recesses of their being, and how we construct these identities, their relationship to our language and behaviors, and the neural architecture underlying them is well beyond my ken. I'm a thermal biologist puzzling my way through fields well outside of convective cooling. I do know I like makeup, and I also know that's not what makes me a woman. The question is, what does?