Frances Bean Cobain -- I Hate Nirvana ... and My Father's No Hero

Musical taste trumps DNA for Frances Bean Cobain, because it turns out she doesn't like Nirvana -- and her feelings about her father aren't much better.

Cobain told Rolling Stone she's just not much of a fan of Kurt Cobain's old band, instead preferring the likes of Mercury Rev, Oasis, and Brian Jonestown Massacre.

Frances Bean (who only referred to her father by his first name) did single out the song "Dumb" ... describing it as "a stripped-down version of Kurt's perception of himself -- of himself on drugs, off drugs, feeling inadequate to be titled the voice of a generation." She says she cries every time she hears it.

Cobain, now 22, also sounds like she's still angry about her father's suicide ... saying she understands his music inspired a generation, but adds ... without that he'd "just be another guy who abandoned his family in the most awful way possible."