I don't think the word itself is what's offensive; rather it's connecting it to a particular thing which some people cherish. If I'm a fan of ska music and active in that scene, I'm obviously going to take umbrage with "ska is dead", even if it's vastly less popular than its apex. And "dead" is clearly an exaggerated euphemism in the vast majority of cases: even "Latin is a dead language" isn't strictly true.

"Dead" may not be intrinsically offensive, but in practice "X is dead" is at least triggering (by the casual/mild definition of the term). :)