I've occasionally come across this issue and I don't know what I did for this to happen. I have a path that was made using offset path, when I cut and select one of the pieces, the other half gets selected aswell. Any edit or movement I apply also effects the other path and no, the pieces are not in a group, I've already tried ungrouping them.
The paths been cut and a piece has been selected
The other piece also gets highlighted when mouse hovers over the selected path.