>…how exactly CAN’T a cutting point of scissors convey information…
If you are holding the giant handles of the scissors and you want to signify that the British Are Coming by making them snip, you squeeze the handles and some time later the tips cut. Scissoring, in this case, is messaging. The message can’t travel faster than c. In fact, it can’t even travel faster than the speed of sound, as some have noted.
Suppose you were able to order giant scissors with any curve you liked on the cutting edges. You could arrange for a great long length of the edges to do all their cutting with only the slightest bit of angling. Two people standing next to the scissors at either end of this great long length will note that the edges pass almost in an instant. So, you squeeze the handles, and the people see the snipping happening almost simultaneously along this area - but if the person closer to you wanted to change something about the message (which could only be to stop it, because we only have two states and the scissors are in the cutting state now), he would have to try to grab the blades and prevent them from snipping. He’s in the same predicament you are with the handles - he can only influence the other end of the long length at the speed of sound. The cutting point on the scissors is moving along, and he can’t change that faster than the handles already could change it.
Imagine you got the great long length curved a little too far, so that the scissors actually met out near the tips before they met at your end. Now the cutting point is actually coming toward you. Clearly, there’s no way you could alter the cutting point that is now passing you to change what it did a moment earlier, out there.
I think superliminal behaviors in astronomy are a rare real world example of these kinds of weirdnesses.
Another analogy - you can aim a laser pointer at the floor, and make the bright red dot zip around. With a big enough floor and a powerful and tight enough laser pointer you can make the red dot move at faster-than-c. So you get two of your friends to stand millions of miles away where they can see the dot going between them at greater-than-c. You can aim the laser, or turn it on and off, and signal your friends that way, at c. But when the dot goes past one of your friends and towards the other one, the first friend has no way of changing what the other friend is about to see.
Somebody traveling between the friends at the right speed will see 3 dots, one at each friend and a third one traveling in the direction from the friend who got the dot last and toward the friend who got the dot first.
It is confusing to do these thought experiments, but if you look up “world lines” and coordinate transforms in cosmology, they are used there.