Are you so clueless that you think you always have a 120Hz signal just because you have a 120 Hz screen?
Think about it in terms of FPS in a video game. If your graphics card can only deliver 40 FPS in a game are you playing at 120 FPS just because you have a 120 Hz monitor?
Why is it any different with a Blu-ray player? The Blu-ray DVDs are almost all 24 FPS, some are 29 FPS. There are some 720p videos that are 60 FPS but they are very rare.
Most blu-ray players only output 60Hz max.
So please tell me how you can view a movie at a true 120 frames per second when the source is 24 frames per second and the player can only output 60 max...
Your screen may be a 120 or even 240 Hz but it's actually displaying the same image more than once because the source is not that high of Hz.