This kind of question ("Tell me about your weaknesses," "Tell me one thing you think your (current|ex) manager could do better to manage you," &c.) often test for one of two behaviours:
1. Diplomacy and tact, and/or; 2. Ability to regurgitate a template answer you can find in any rudimentary book on handling behavioural interviews.
It takes extreme skill to get a candid answer out of everyone, so it is easy to get gamed by the tactful people at the expense of people who don't read a book about how to ace the interview.
But people who don't read books about interviews can be very competent at their actual jobs.