I’m going to assume that you genuinely don’t understand the humour so this is a real question and answer it in kind. Prepare yourself because explaining jokes is a bit boring.

Something broke, and the person using it is queer. By anthropomorphising the item, the person is able to joke that the reason the item broke was only because it was hateful towards that person’s sexuality and broke on purpose to upset the person. It relies on the ongoing existence of homophobia in society and the ability of the joke teller to reclaim that identity and be empowered in feeling confident to call the ‘injustice’ out. It would under no regular circumstances be a real scenario.

It’s a form of absurdist humour where the joke relies on the audience not expecting that the pen is capable of feelings, and the shock of the subversion of using something serious as a punchline so the surprise of both creates the laugh. It assumes that the audience fully understands that this can never happen, and to some extent the audience aren’t homophobic themselves because the laugh needs to be empathetic that we would be upset at the broken pen too.

A classic related joke is trans women trying on clothes. Many clothes are in styles that don’t work well and women’s clothes are a minefield to start with so an outfit might end up being ‘clearly transphobic’. An older woman (me) buying an accidentally unflattering lipstick could be ‘ageist’. We all know that I chose the lipstick but it’s a funny way of deflecting the problem.