Is it considered a derogatory remark when someone calls a psychologist or a psychiatrist 'shrink'?

The noun shrink is shortened from headshrinker, in whimsical allusion to that shamanistic art, perhaps still practiced in remote jungles. Not in the least bit derogatory, it refers to the old-fashioned conceit that a swelled head is the root of most people's problems.

Some mental health professionals find it insulting, and others are amused. It has always seemed to me that an individual with a healthy self-image wouldn't be bothered.