I've dated both men and women. While there is definitely a certain "type" of person I go for (hint: bad "boy" transcends gender) the similarities in the relationships end there. Asking who is the "man" in a relationship assumes that somebody needs to be playing a masculine role in order for the chemistry to function. The reality is that women, femmes, and non-binary people don't need men to be happy and fulfilled within relationships. In fact, I am actually much happier and more fulfilled without them!
Asking who the "man" is in my relationship with another woman is also super reductive because it presumes that all relationships function on a like heterosexual ones do. This isn't so much offensive as it demonstrates the absolute lack of imagination that's endemic to heterosexual society. Why does someone need to be a "man" in order for a relationship to work?
Personally, my heterosexual relationships with cis men were characterized by imbalances. Asking who is the man in a lesbian relationship implies that we need someone else to be a "masculine" figure. But in my experiences, relationships with men have been fraught with toxic masculinity. My past male partners have demanded emotional labor from me while dismissing or gaslighting me for having feelings in the first place. Sexually, I was unfulfilled. If I mentioned that I needed more, then it would trigger insecurities about prowess in my male partner. My relationships with women have had exactly none of these qualities.
Not only is it absolutely ridiculous to ask who is the "man" in a lesbian relationship, it's also a completely outdated question considering all we know about gender now. A person can possess both masculine and feminine qualities regardless of their biological sex. Even biological sex is infinitely varied. The idea that we exist in a binary — where people are either "women" or "man" — is completely false. Honestly, some days, I feel like a woman. Other days, I feel like a boy, and other days I feel like neither. I have a shaved head but I sometimes like wearing a full face of make up and sometimes I like wearing boys clothes. I've passed as a boy before. Does that make me the woman or the man? I am simultaneously both and neither. And I don't care whether anybody else understands that, as long as I understand who I am within myself.
The only reason society continues to operate within this simplistic, black and white world is to oppress and erase the range of queer identities a person can inhabit. And honestly, I don't really care to explain my relationship or my identity to inquiring minds.
The truth of the matter is that most people who are wondering who the "man" is in my lesbian relationship are probably curious about my sex life, and want to fuel their own fantasies. But to me, the secret life of my lesbian relationships need to remain clandestine. This is not because I am ashamed of them or even because I am fearful — no. It's because people who insist on living their lives within a binary and pursuing only heterosexual relationships don't get to access the healing magic of a queer relationship — not on any level. That is a knowledge that they have to pursue on their own, if they want to receive it.
It's not up to queer people to live their lives in a way that will be comprehensible to mainstream heteronormative society. It's not up to us to explain it or even have to be intelligible. If you're curious about a queer person's relationship, go out and start exploring your own boundaries of gender and sexuality. You might just find they are way more fluid and variable than you think.