60Hz will produce judder in 24 fps content, and judder means mismatched motion from uneven content frame persistence.
When you need to somehow display more or less 24 frames per second (23.976 actually) on a 60Hz display, you need to repeat frames since 24 obviously isn't the same as 60. But you can't just repeat all the frames consistently for the same number of refreshes (5 frames for 120Hz panels (5*24=120), 6 frames for 144Hz panels (6*24=144)) since 60 isn't divisible by 24 (60/24=2.5, and you can't repeat a frame for half a refresh).
In this scenario, what players do is send half the frames 2 times, and the other half 3 times. If odd frames are repeated for 2 refreshes and even frames for 3 refreshes, you end up with (2+3)/2 = 2.5, which is exactly 60/24.
However, if you're repeating half your frames 3 times instead of 2 times, you're displaying them for 50% longer than the other half, and creating motion unevenness that wasn't intended.
This phenomenon can be represented visually:
Or, for even better understanding, a video:
There is a reason TVs nowadays are pretty much all 120Hz, and that's because it's the refresh rate that works the best across a wide range of content. Repeating each frame 5 times in a row doesn't create any motion problems, unlike repeating half of them for 50% longer.