It sure sounds like you're the one being overly sensitive given that you're describing two equivalent states of affair and finding one of them offensive because you don't the words attached to it.
Well of course, there's a difference in connotation of blame between "privileged" and "disadvantaged", even if they both refer to the same relative difference. It's as if the terminology of "privileged" is purposefully trying to offend.
It is. The -point- of the term is to reverse the usual dynamic between the privileged and the disadvantaged. What that dynamic is depends on whether you see the categories in this comparison as only two (the haves and the have-nots) or three (including a "normal" category which lies somewhere between the two), or perhaps as a spectrum (where privileged and disadvantaged arguably lie at the extremes of the bell curve).
I'm saying I consider it insensitive to not care what effect your choice of words has on how people perceive things. If you think that makes me 'overly sensitive', then I'd recommend reflecting a bit on who is hurt by bad messaging. And if you don't believe me that it's bad messaging, just look up the studies on the effects of framing racial inequality as privilege.