Fixed step free style push hands training disallows the feet of the practitioners to move. The objective is to force the practitioner to yield or neutralize the opponent's attack by moving his/her body rather than getting away with footwork. In a competition, the one moving his/her foot first loses the match. It is a popular training in Yang or Cheng Man-Ching style Tai Chi.
This is just his preferred side since he is right-handed. Of course, one needs to practice both sides (right foot front or left foot front) during training.