Why do I have to manually spin blower in oder for the a/c to work?

Defect in the motor... time for a new motor.

Presuming you are talking about the indoor fan motor: Try changing the capacitor. They are inexpensive & easy to replace. If that doesn't help, it's probably time for a new motor.

I would most certainly start with the capacitor, as mentioned above. If that does not fix the problem, new motor for sure.