Strange exchange of an active layer upon moving its contents by the move tool (Mac Ventura)

This has happened to me a few times with different PS versions, this time by the latest one: I have multiple layers in a document. When I first activate the target layer the content of which I want to move to another location in a photo, and then try to move the contents, the activation of the target layer disappears and "jumps" to another layer the contents of which are now being moved. I have never figured out a good solution to this problem. Basically, I need to build the photo from the start. Ideas what I could do to avoid this situation??