Annoyingly insensitive (6)
I believe the answer is:
obtuse
'annoyingly insensitive' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for obtuse that I've seen before include "Slow of understanding" , "Dim-witted" , "'Dense, slow (6)'" , "Thick, blunt" , "Angle greater than 90 degrees" .)