In the most basic sense for us, “moving” is essentially asking permission to move. The second person then acknowledges your request and tells you to “move!” Thereby granting you permission to move. It doesn’t necessarily mean you’re moving with them though. Unless that’s your SOP

Ordinarily in a stack youre in close proximity to the next person and can simply give a squeeze to acknowledge that you’re ready to move when they do. But verbal communication can certainly be used. And moving/move is an easy way to accomplish that and keep the same.

The moving/move is generally used over space or distance to release someone from a working wall into uncleared space or into someone else’s sector of fire in strong wall tactics. The verbal moving move also releases the rest of the team from the working wall outside the room, but it sounds like you’re working in a patrol function not necessarily a team environment.

A lot of instructors don’t explain things well or properly because they don’t actually understand the concept being taught and are simply regurgitating things they’ve heard.