It seems like he wants to make sure he's not incentivizing being sick or in crisis or staying sick or in crisis. However, he's taking it to the next level in a way that makes no sense. I understand that he has concerns related to the diagnosis you don't like to name. However, he's just ended up incentivizing being dishonest that you feel bad. Honestly, I think when therapists control session frequency, it always creates an incentive for a client to be dishonest.

In any case, he must not think you actually feel bad and that your expressions of feeling bad are "acting out." This is a thing that people believe about people with a certain diagnosis, and it can be true sometimes. He might conceptualize you feeling bad as purely longing for connection with him. Following this line of thought, he is offering you a reward for not acting out. It would make sense if your problems could be solved purely by modifying your behavior.

I'm not a fan of the way your therapist approaches anything.