The most obnoxious thing about "problematic," besides the fact that it's vaguely tossed around willy-nilly, is that it describes the offense as a trait of the "problematic" thing, rather than a reaction of the people.
It's basically the difference between "that's offensive" and "that offends me." The former is stating how one feels about something as an absolute truth, while the other acknowledges the subjective nature of offense.
With "that's problematic," you're trying to hide the fact that what you really mean is "I take issue with that." It doesn't matter if 400 people aren't offended by this, 5 people are, so it's "problematic," a trait of that thing we're condemning.