Speculating, one possible reason would be that it can then make balance corrections by pushing (making the leg longer). A wider stance would require making balance corrections by making the leg shorter.
It's what you generally see in nature too when (catlike) animals are bounding: http://cincinnatizoo.org/wp-content/uploads/2012/07/sarah_ru.... Front paws go between the rear ones, etc. Rear ones are used for the brunt of propulsion, front ones for balance and direction etc.
