Diagnosis
You are using an older HDMI cable (likely HDMI 1.4) or have the monitor plugged into the wrong port on your PC (like a motherboard port instead of the graphics card).
How to Fix It
Use the DisplayPort cable that came with the monitor. If you lost it, buy a certified DisplayPort 1.2 or later cable. Connect it to a DisplayPort output on your dedicated graphics card. Windows will then detect 120Hz capability automatically.
If That Didn't Work
If you must use HDMI, you need a high-speed HDMI cable (HDMI 2.0 or later). Then, you must manually create a custom resolution in your GPU control panel (Nvidia or AMD) to add 1920x1080 @ 120Hz.
Heads Up
Many laptops have HDMI ports that only support HDMI 1.4, which maxes out at 1080p 60Hz. On a laptop, 120Hz will only work via DisplayPort or USB-C with DisplayPort Alt Mode.