LucidNarwal's Questions (2)

I suddenly remembered a manga I read time ago and I'm trying to make my friend remember too, but I can't find it.

What I remember:
-The main character was a guy with issues. He slept with assholes, among them an older classmate or a teacher, I don't remember.
-His mom had died and probably that had to do with his issues. He lived or at least had a good relationship with his uncle, his mom's brother.
-The guy ends up falling in love with his sister's boyfriend.
-Besides that, I'm pretty sure the title included 'bird' or 'cage' or something alluding to those.

At this point I might've made the manga up lmao. I'd be super glad if you know it and let me know the name (':

I'm not against couples with static roles, but I'm sooooo done with the physical and behavioral stereotypes that come with it.

So, any recommendations for couples who switch?
The only ones I've read so far were Thirst (<3) and Wagging the tail (I kinda disliked that one because one of the characters), but I'm holding hopes for Our Sunny Days and The pizza delivery man and the Gold Palace.

I hate that it's considered a trope and that it's so rare to find, and that people freaks out when it happens or is hinted :c