Well... because there are many songs about break-ups.
I have often felt like I can't quite relate to songs like that because I haven't experienced it.
Despite the fact that I have sometimes written poems and stuff about break-ups, but that has more been me imagining what it is like or been inspired by break-up songs and other stuff. (which might also be the case for some artists who make songs like that)
There was one time though when I got rejected by the guy, I had a crush on, and I listened to some songs that made me think of him, including break-up songs. Or at least I listened to one song, which was Lee So Young's "Grace". (but some of the songs, I listened to, were also kinda random)
I remember even writing kpop fanfics back then that had rejections and similar stuff in it. (back then when I wrote a LOT of fanfics in that fanfiction section of the AKP forum)
I guess for some artists, who have experienced having a break-up, it can perhaps be cathartic to write songs based on their experience with it.
But for the person that the song is about, it might be awkward if they know the song is about them...