This word is overused, and not really all that clear, in my opinion. It suggests that the subject or word constitutes, or presents, a problem or difficulty.
For example if you would say that X is a problem, then rather than explaining why, you would just say "it is problematic".
I think this is an issue because the word "problematic" doesn't even refer to the stated problem but is just a way of classifying it as being; difficult to answer, hard, taxing, troublesome, tricky, awkward, controversial, ticklish, complicated, complex, knotty, thorny, prickly, or vexed. It is really just an intellectual cop out.
A better definition would be to say that the problem is "open to debate". That suggests that the question may not ever be resolved but isn't just a push back that one is not even willing to talk about it.
Using the word "problematic" is not an issue that I am suggesting is "problematic". I am just saying we ought to just "stop using the word".