95% of the music I listen to that isn't classical music, and thus probably from several centuries ago, was released after 1996. The notion that "good" modern music doesn't exist is misguided and frankly rather silly. Where that sentiment might have some bearing is if you append "well known" or "popular" to it - the music aimed at the general populace is, for the most part, pretty much crap, saying that isn't even remotely controversial.
But if you're laboring under the belief that all modern music can be defined by the crappy stuff you hear on the radio, what that says about you is you're too lazy to go looking for those rare gems and have settled for blanket assumptions that make music snobs like me laugh at you.
Also music in the 90s was, as a general rule, awful (though I would take 90s boy-bands over what passes for pop these days in a heartbeat, which says a lot about how terrible modern pop is).