If the tugs apply the same bollard pull of say 15 tonnes each, it is to a position 80m fore and aft of the pivot point. Thus two equal turning levers and moments of 80m x 15t (1200tm) are created resulting in even lateral motion and no rate of turn.
With the ship making steady headway, however, the pivot point has shifted to a position 40m from the bow. The forward tug is now working on a very poor turning lever of 40m x 15t(600tm), whilst the after tug is working on an extremely good turning lever of 120m x 15 t (1800tm).
This results in a swing of the bow to starboard.
The efficiency of the tugs will change totally when the ship by contrast makes sternway. Now the pivot point has moved aft to a position 40m from the stern. The forward tug is working on an excellent turning lever of 120m x 15t(1800tm) whilst the after tug has lost its efficiency to a reduced turning lever of 40m x 15t(600tm).
This now results in a swing of the bow to port.