So I'm gonna try my best to explain this tumblr faggotry, like the logic behind it, as well as why it's idiotic (besides the obvious reasons).
So the concept is that, because they believe pronouns =/= gender, that anyone of any gender identity can use any pronouns. In this case, a "he/him lesbian" is a woman (identifies as female) and uses he/him pronouns, and is also attracted to exclusively other women. A "she/her gay" is the same but with gay men - a man (identifies as male) and uses she/her pronouns and is exclusively attracted to other men.
The reason this started is because some idiot stated that, historically, there were cases of lesbians using he/him pronouns and gay men using she/her pronouns. The post(s) stating this became popular and reblogged and soon several people began to follow this mindset. Their arguments for this are: gender is a social construct, pronouns aren't gendered, and there's historical precedence for it.
Well, those first two are bullshit and could be argued all day at night with tumblr users, but that's not the main reason why people started this - because they believe their's historical precedence for it.
In a way, they're not wrong about that: yes, historically, there is precedence for lesbians, particularly butch lesbians, using he/him pronouns, and gay men, particularly feminine gay men, using she/her pronouns. However, they ignore why this was a thing and why it is no longer a thing.
As someone else already mentioned, one reason why there were "she/her gay men" and "he/him lesbians" is because transgender people were unknown and the public didn't understand them - so heterosexual transgender men were "he/him lesbians" and heterosexual transgender women were "she/her gay men". Which is, ironically, based on historical ignorance towards transgender people and "transphobic". So tumblr played themselves, there.
Another reason is the existence of drag queens/drag kings. Of course, tumblr thinks drag is transphobic, so they ignore that drag performers only use the opposite sex pronouns while in their drag persona.
The last major reason is because of like, actual homophobia, where lesbians were referred to with male pronouns and especially gay men were referred to with female pronouns in a mocking, discriminatory way. So sometimes they embraced it.
Sorry, this was an autistic spiel, and probably sounded painfully sjw. But to try to grasp this shit you kinda have to see where they're coming from - even if their logic is shit. It makes it easier to make fun of for myself personally, because you can turn it on them very easily, like, "oh so you're a transphobe then," and watch them squirm.
TL;DR: tumblr thinks girls can use male pronouns and boys can use female pronouns because they think it's a historical thing, ignoring how it's based on historical bigotry.
Sorry again for the autism, to make up for it here are the "she/her gay" and "he/him lesbian" flags:
View attachment 484060 View attachment 484061
And y'know what? Here's a bunch of other stupid tumblr flags. Lots of images, note that the labels are exactly what the creators labeled them, I didn't make these up myself: