Timing Is Everything

One of the more important principles of using keyboard modifiers is that the same key will have different effects, depending on when you use it. For example, with the Direct Selection tool (A) active, holding down the Option key (PC: Alt key) will select the entire path. If you don't let go of the Option key when you drag, you'll get a copy. So in this case, to move a path without copying it, press-and-hold the Option key and click on the path, then let go of the Option key before dragging the path.