Personally, I'm not a big fan of breakup songs or excessively whiny songs, however, if you feel like it, write it. First of all, it will probably make the person writing it feel better (as Heretic already pointed out).
And also, It's definitely better than just writing a song about some topic that you don't care about, because honest music is, whatever genre it is, a hell of a lot better than some song that was created without any personal involvement on an emotional level but mainly to please a broader audience.
Of course, still, just because that excissively whiny song you wrote might have helped you and be honest, that doesn't mean I like it. It's just preferable to fabricated pop music.
That said, I also have to say this because one of my favorite songs, Prayer To God by Shellac is a breakup song, even it isn't whiny but just damn cynic.
I also especially agree with Mechorg's statement "write about whatever the hell you want" if you interprete it in a different way (which would be political): It's also okay to write racist or otherwise offensive songs. Not exactly because I would like it (I probably wouldn't, with the exception of Anal Cunt or Burmese songs and only because they're so over the top they can't possibly be serious anyway), but because the freedom to write about whatever the hell you want also applies to idiotic ideas.
Of course I'm still in favour of beating these people up for their ideas, especially if they're Nazis, but that's just good ol' tolerant me.