The tape doesn't stick to the threads.
You should be able to unscrew the joint and the tape should just peel right off. When you tape, make sure you go in the direction that the female side will screw so that the female side doesn't push against the trailing edge of the tape but rather goes with it.
Also, only put enough tape to cover the threads completely - but not excessively (2 complete revolutions usually works for me - others and pros may differ).
Third, you should consider using pipe joint compound. Some people prefer joint compound to tape. Some prefer tape to compound. Some prefer both...