To answer OP, this is why:
https://www.testufo.com/
Which one looks smoothest to you? That page can only show you what your current refresh rate looks like, or slower. If you are viewing it on a 60Hz signal, then it will show 60FPS, 30FPS and 15FPS. One would assume that >60 will be even better - to a point. That's debatable, but I believe for most people 144FPS is obviously better than 60. And you receive more visual information at higher refresh rates. You are literally missing reality at lower refresh rates. Take the above ufo animation example at 60Hz and 1920x1080 (what I'm currently viewing at). The top ufo, which represents 60FPS animation, is "jumping" across the screen 16 pixels at a time and traverses the screen in 2 seconds (960 pixels per second). Double the FPS to 120 and it will be jumping 8 pixels at a time to reach the other side in the same 2 seconds. There's more information there. Not only will it appear smoother in motion, but it is a better approximation of the actual location of an object as defined by the game engine. At 60FPS new frames are displayed every 16.7 ms - if they are ready. The game engine might be slightly late at calculating the next frame and just miss the current refresh of the monitor, so it will be rendered 16.7 ms later on the next frame. By that time the object is out of place. In the above example it will be out of place by 16 pixels. The result is that in an FPS shooter the enemy's bullet or grenade is closer to you than you think!