A well-known psychiatrist in a small town encounters with the mental status of different patients wanting to become professional writers, but he realizes that his advice to them won’t work.

Agreed with Richiev and DPG.

The plot isn't clear, what specific event motivates him and what exactly is he motivated to do?

>>>but he realizes that his advice to them won?t work.

FADE OUT to the? CREDIT ROLL? -- Is that how the story ends?? Or is it the inciting incident for a plot to follow?

If the former, a logline should never give away how the story ends.? If the latter, then what becomes his objective goal as a result?

What is the goal of the lead character?

(I just re-read this. Does the lead character want to become a professional writer? Or does his patients? The first time I read the logline it seemed as if the patients wanted to become professional writers but now I am not so sure that is what you meant)