I think I started hearing the word "inappropriate" being used—ahem!—inappropriately back in the 1980's when I was doing volunteer work for a social service agency—the type of place that is populated by psychologists, social workers, and their clients—as well as amateur "helpers." (I was in the last group.)

The dilemma you have when you work in a place like that, is that people who have done terrible things (drug abuse, child abuse, spouse abuse, etc.) are coming to you for help, so they can (hopefully!) quit doing them. If you react with obvious horror and disgust, especially before you gain the clients' trust, you will drive them away, and you'll never be able to help them.

So you evolve an ethic that says you must suspend or moderate judgment, at least temporarily, at least about anything the client did before he entered your door.

Imagine this dialogue, in a group therapy or "support group" session:

CLIENT #1: …and after that, they put my daughter in foster care.
CLIENT #2: Jeez! That's disgusting. Guys like you ought to be castrated!
FACILITATOR: Now, now. We don't make value judgments here. That remark was inappropriate.

OK, I made up that dialogue. Maybe a real therapist would have said it with more finesse.

The irony is, people make value judgments all the time. You can't help it. To call a remark "inappropriate" is itself a value judgment.

I think "inappropriate" became popular because it's a relatively mild word. It's a lot less likely to cause offense than "shut up!"