Not entirely sure about that: go to Settings > general >
Use Side Switch for: ( choice of ) Lock Rotation OR Mute.
You can only choose one by tapping on it (resulting in a checkmark next to it) - if you choose the other, then the first checkmark disappears.
Edit: the above makes sense as it seems to be a toggle switch - toggling back and forth - or, choice of one or the other......
And:
When the side switch is set to mute the Control Center become lick-rotation and vice-versa.
My side switch is set to mute AND the control center is turned OFF / not activated. All I do is turn the iPad horzontally or vertically and the screen follows automatically. No Control Center or Side switch needed.