men probably don't like bkg much for two reasons: he's narratively unmasculine and an ego competitor.

not everyone engages with fiction through extremely blatant projection, but many do, and it's very common amongst mainstream, non-transformative fandom people, who tend to be predominantly men. plenty of exceptions of course, but we're talking in generality, probably cishet, too.

since bkg is narratively unmasculine, he doesn't have an arc that is appealing to men who are, whether consciously or unconsciously, looking to find a character to project onto. difficult to want to see yourself as the guy who keeps getting kidnapped, or is learning empathy.

bkg's ambiguity in terms of how much he says about himself also tends to be another barrier to being able to put yourself in his shoes.

more women probably like bkg because of this odd subversion of masculinity, as it may feel more reflective of themselves, hypothetically.

i'd also say that many women are less used to seeing themselves represented properly in fiction, and thus are more willing to contend with character ambiguity. but again, this is conjecture.

the second reason men probably don't like bkg much is because he's an ego competitor.

by that, i mean that, since men have difficulty projecting onto bkg, they see him as a rival instead. esp. those who project wholly onto deku, they see bkg as a threat to themselves and their ego. bkg is their opposition, he refuses to appease them.

he's not good for projection, due to his narrative unmasculinity, but he's not good outside of projection either, as a decidedly aggressive male. being aggressive alone isn't bad, it's the fact that he's male, that's what threatens the ego.

(plenty of men find aggression attractive... in women. that's why you probably see so much mitsuki porn. bkg's personality suddenly becomes very attractive to men when he's swapped to female. he'd no longer be a competitor but a prize in that circumstance.)

women, on the other hand, might find that appealing. on the surface, he's a repentant bad boy personality -- isn't that attractive? he's not viewed as competition.

so, men don't like bkg because he's hard to project onto, and his personality doesn't appease them otherwise.

two of the biggest ways people enjoy media, and bkg fails on both counts amongst men.

but, amongst women, speaking generally, he seems to excel on both counts. his personality isn't abrasive to most women, and may even be attractive, so he very easily appeases that crowd.

as for projection, i think the idea that he is a fairly androgenous/masculine character being forced into unmasculine storylines... resonates with many women and/or queer people? that dichotomy of personality and society. inner self and outer presentation.

anyway, none of this is word of god, just late night rambling. but the sheer difference in how much women love bkg compared to men is really remarkable.