Let's say we have a metal rod of consistent density sitting flat on a frictionless surface. I intuitively understand that if I push one of its ends away from me, (at a right angle to the length of the rod) it will spin on the surface.
I've looked at What is the proof that a force applied on a rigid body will cause it to rotate around its center of mass?, and If I push or hit an object in space will it rotate or move along a straight line? and Farcher's answer to the second question comes as close as anything to explaining the phenomenon the way I'm requesting, but I still don't entirely understand.
Like I said, I understand intuitively what will happen, but when I try to picture the individual particles of the rod I can't understand why the rod rotates instead of just moving off as a whole away from my impulse. If I cause part of the rod to move up, shouldn't all of the rod follow, just like if I grab the rod at its edge and lift it up? Obviously that's not what actually happens though. I know it must have something to do with torque, leverage, etc. but I still can't explain it.
I hope this wouldn't be considered a duplicate question since the main difference is I'm asking for a layman's explanation, not a mathematical proof. If it is the case that it can't be explained without a rigorous mathematical proof that's fine, but in that case sorry for the duplicate!
Thanks for any assistance!