I think it's translation error. The mistranslated of "break up" here would be the end of their relationship as "friend". Cause if you read it there's a scene where mc saying that ml ask mc to live together so ml can sleep with mc (of course that's just how mc thought) and that's why they parted ways and mc cut off his communication with ml for 10 years
I actually don't think its a translation error, because the dialogue goes back to the "break up" term later on when he can't say the phrase to his (ex) boyfriend due to trauma. I seriously think the author just changed his mind and made up a shitty explanation like "friend break up" to make up for it. Either way, it seems very poorly written.
Since I was so curious, I look up at the raw and here what I get.
The first chapter where the flashback show that ML asking "should we break up" was actually written as "우리 잘래?" In the raws and it's actually means "shall we sleep together?" which is match with the flashback where ML and MC about to be together in latest chapter (I forgot, I think it's 7?8?).
And their relationship from the start was just friend. What makes MC trauma is because ML was the one asking MC to live together and they did live together well just like a good roommates. When ML suddenly asking to do sex and somehow forcing it to MC it leaves a bitter memory to MC and think that ML asking him to living together so that ML could sleep together with MC and just want MC body.
So the summary is... It is a mistranslation

Did the author decide to change the plot midway? lol. At first mc says he has a trauma from the ml because the ml broke up with him out of the blue. And later when they confront each other in ch 6, it turns out they were never together, and ml pounced on the mc out of the blue while they were friends and mc was dating someone else. So where the hell did his "break up" trauma come from? This is so fcking werid lol.