It bothers me that she's being so submissive and that Clark isn't interested in learning more about her. Johns barely even lets Diana talk about her own life; he has Clark explain it for her on multiple occasions. Diana has noticeably less dialogue in their scenes together.He goes to the major visual method he uses. If he's dominating the relationship then its because she's allowing him to. Remember, loving submission. She's the one asking for information about him. Apparently he doesn't feel the same lack of information about her.
It would bother me if it happened with Superman, too. In fact, the situation you described happened on Smallville with Clark and his friend Chloe Sullivan in a scene from the episode "Infamous." Chloe isn't a superhero, but she did tell Clark about a dual identity (and in a later episode credited herself as his inspiration):After all, she doesn't play the dual roles he does. She is who she is and now seems to be looking to be more than just herself. I don't think this would even get a notice if it was reversed. Superman going to Diana Prince (instead of Batman) and asking about secret identity and she suggests glasses since they work for her. Sure, why not. Right there the first thing you see. But if ever Diana learns something from a male, she's being disrespected as a female hero.
Clark: If you consider complete invasion of privacy a perk. Though there was this one moment right after I told Lois the truth about me. I thought everything would be okay. Thought I could have it all, but I was wrong.
Chloe: You know, Clark, maybe you can have your cape and wear it, too. Say that Clark Kent, the unassuming journalist, buttoned up in a starched shirt and tie, but then, when he's playing the hero, he...
Chloe: You know, in every epic tale, there's always one person who believes in the hero first. Someone who helps inspire them to greatness. And maybe it wasn't just a fluke with you. I've been thinking that's my true calling; finding heroes and helping them realize their true potential beyond the reach of Watchtower.
I had problems with Chloe's role in these instances just as I do now with Clark and Diana. I'll reiterate that Diana learning from Clark isn't, by itself, problematic. It's the accumulation of factors that makes this potentially a step too far. Diana was trained by a man (Ares). She was encouraged to be more of a team player by Superman. This whole process of Superman informing Diana about himself is so he can get her to trust him, which Johns had Superman and Wonder Woman equate with helping Diana trust others and thus her instincts better. The scale is tipped too much on the side of other people, especially men, forming Diana. I'd like to see the scale tip more the other way soon.