I think it's because we've been conditioned to process movies specifically at that frame speed. Like our eyes watch something filmed at that speed and our brain interprets it as "Oh, this is a movie."
This was in the comments. I don't know if it's legit or not.
The eye sends information to the brain somewhere between every 1/48th of a second to 1/60th of a second. Which, surprise, surprise, is the same as shooting 24 fps to 30 fps. These frame rates have a shutter speed of 1/48 and 1/60 respectively so the motion and motion blur is very similar to our own eyes. Shooting at 48fps has a shutter speed of 1/96th. Which I clearly stated above. That is why the motion captured at 48 fps looks UNNATURAL. Because it's not what our eyes do.
First of all, the human eye does not work neatly in fps, it's a continuous stream of visual information. Humans can detect flashes even as brief as 1/200 of a second, but can be fooled into seeing smooth motion at much lower framerates (eg the 24fps of cinema)
I believe what this person is referring to is the subjective reasoning that most people can't differentiate between framerates higher than about 50-60fps, a figure derived from gaming where it starts to look jerky roughly below that point, but keep in mind that's because there's typically no motion blur to compensate for the inbetween motion to fool the eyes. If this figure is infact derived as I suspect (which I'm fairly sure it is, as I've found no other evidence supporting it), then it would actually ironically prove the opposite point, as a video game at 60fps has a shutter duration of 0, even shorter than the "unnatural" 1/96 like he's suggesting.
Even if we take this figure of the brain registering 1/48 - 1/60, this does not equate to the shutter speed of a camera. FPS =/= shutter duration. Both 24fps video and 48fps video generally use a 180 degree shutter, so the shutter duration works out to half of the video frame for both systems. This has no direct correlation with framerate though, as the shutter speed can vary, and you're still only getting 24 discrete frames, not 48. A lot of action scenes use a much shorter shutter time (a look which just looks stuttery to me at 24fps).
Even ignoring the flaws in his logic, it would only work if you had 48 discrete frames with a full shutter duration, not 24 discrete frames with a half shutter duration (which both work out to a shutter duration of 1/48 of a second for the sake of the discussion).
I'm not sure if that post makes any sense to anybody but me. Sorry.