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Erm... you mean a perfectly normal relationship in which the girl is an Action Girl? First trope I thought of was Understanding Boyfriend, but after a glance at the example couples, I'm confused. What do you mean by "rough around the edges"? Women in general are not dolls (fictional women who are perfect dolls are badly written) - we have opinions.
^^ judging from the inclusion of Jade and Beck, I have some context. Beck is a laid-back nice guy. Jade is an edgy, dark, morbid, often very mean and sarcastic type. Hence "rough". I really don't think there was a reason to imply misogyny here.
Currently Working On: Incorruptible Pure Pureness
Haha no misogyny at all. The women in these relationships usually take no shit, lead the relationship a little more than the man, or are tomboyish in nature. Women aren't dolls but sometimes fiction makes them out to be so much that they become the poster child for what women do in the relationship, which is often taking the back seat
Exactly! So what you mean is a perfectly normal relationship of a somewhat choleric woman and a guy who loves her the way she is. Is that a trope? Not sure.
Examples of couples: Beck + Jade - Victorious Max + Kyle - Living Single
the trope where the girlfriend is rough around the edges, and the man still loves her and finds a way to put up with it. the girl doesn't necassarily push him around, but she can confidently voice her opinion and he respects it and goes with it