I don't think what emo is. I know what real emo is.
If you feel like doing some research wikipedia it or something. Emo was a break off of hardcore music in the mid 80s and continued on until the mid 90s with some bands still playing the origianl sound today. Real emo had nothing to do with "breaking up with girls, I want to kill myself" type stuff. Listen to Embrace, Indian Summer, Native Nod, etc etc and tell me they sound anything like what you (and I mean people in general these days) think emo is.
What people call emo today is mostly crappy pop punk (Panic at the Disco,etc) and crappy post hardcore.
Well your defenition of emo is way off from what it really is. But I guess it fits right into the mainstream defenition these days of emo... which is a joke in itself.
Oh, and Modest Mouse are just and indie rock band.