My gears get stuck when i move from gear --> neutral on 2003 Hyundai Tiburon

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80% of the time, the gears shift very smoothly; however, when i want to park and my car is still in gear, sometimes it gets stuck and im forced to use excessive force to place it back into neutral. I dont know whether i need to change the clutch, the gearbox, the flywheel or its just some basic liquid .. but my mechanic wants to charge me like 800$ just to fix the clutch. Please someone help i dont know how to stop this and its recurring more often.. thankfully it doesnt do it as often while im driving and i need to gear down, but i need to resolve this as this is the only problem with this sick car!!
(1) Answer
There is a simple test for clutch vs trans.

with engine off and the car in neutral, shift the trans then turn on the engine and shift the car. If it gets harder with the engine running then it is usually a clutch issue. I used to rebuild transmissions and that is a standard test.