Sometimes Google Maps will not allow me to drag-and-drop to manually change the route. It just pans the map around, instead of dragging the route from one road to another.
This happens when the written directions are expanded to show the details. To re-enable manual rerouting, get rid of the detailed directions. It won't let you change the route because it is displaying the specific roads and it doesn't want to re-draw that panel.
At the top of the written directions, there will be a (blue) panel which says something like "From