Passive Aggressive Personality Disorder is common and frustrating. It is a manipulative technique, seen when people lead you to believe they will do something although they never really intend to follow through, or say or do things that circumvent progress toward your interests. They are victorious when their victims are visibly frustrated.
Deliberate procrastination, or criticism packaged like a compliment, are examples.
Calling them out on the behavior is disarming. They do not like for people to realize what they are doing, and the behavior generally stops, at least for that instance. The behavior will return, so keep addressing it and request a correction.