As a former Supernatural fan (who fucked off around season five when it went to shit), I might be able to translate.
Early in the season, Castiel (dude in the trenchcoat who is potentially?* gay) was trapped in what SamTheEagle so aptly calls Super Hell (basically a void-space with a consciousness residing within it), and the way he got out was to make a deal with the consciousness that he would instantly be deported back to Super Hell if he ever experienced true happiness. Or something. I didn't watch it, but I read stuff.
Anyway, in the scene Castiel confesses his love to Dean (constipated looking dude) which will send him straight back to Super Hell because he's just so happy to tell Dean that he loves him even if it's not at all reciprocated (which is being seen as quite offensive and tone deaf, not least because confessing your gay love for someone you think is straight is usually horrifying, not something that makes you happy) and somehow this saves Dean from a thing, I think? I lost the plot at this point and nobody is talking about anything but that one scene so it's hard to tell what else was going on.
So basically the biggest issue is that killing off a character immediately after making it clear that they're gay is a HUGE homophobic no-no. Media has a massive history of killing off gay characters - it's referred to as Bury(ing) Your Gays - and it is often used in media to demonstrate homophobic ideas (that gays don't "get to" be happy, that gays should be punished with death for homosexuality, etc). In this case, sending Castiel basically to the worst Hell ever described on the show is a pretty clear message: If you're gay, you go to Hell. Pretty obvious homophobia.
There's also the fact that this is how they capped off a good ten solid years of what the fandom considers "queerbaiting" - that is, they've been teasing the relationship between Castiel and Dean basically since Castiel showed up in season four, encouraged by the fans who love the pairing, and then they end it with a "love confession" where the kind of love that is meant isn't even stated and Dean has zero reaction whatsoever. It's a pretty nasty way to pay back the fans that basically kept the show alive for ten years past the expiration date.
I think there's more to it and to people's complaints, but that's kind of the basics.
Personally, while the homophobic "bury your gays" bullshit always infuriates me, I think the most offensive part about the whole thing is the terrible acting. Jensen (Dean) could have been replaced with one of those life-sized standees and no one would have been the wiser, and Misha (Castiel) was overselling it so much it was truly cringeworthy and felt like he was parodying his own lines. But to be honest, I'm not sure how anyone can still take the show seriously after they pulled a season of "the boys versus god" immediately followed by "oh shit we ran out of stakes wait what if it was the boys versus god's evil sister who is totally scarier and more powerful than him!"
(Also, I'm really not sure how anyone is complaining when Supernatural has literally been homophobic as shit all along. Like, the entire time. Anyone else remember Corbett? No? Just me?)
* They really don't make it super clear that he meant romantic love, so this is pretty up in the air. Even when they're being homophobic on Supernatural, they're being extra homophobic by making it clear what they want the fans to understand in a scene but being too cowardly to take it all the way.