Are you sure you're looking at WC Swing? We don't have a step called "Push", we have a "Sugarpush", which is step #6 in the syllabus, the one you describe below.
The ballroom community sometimes considers the Sugarpush to be the basic action, but the WC Swing community doesn't typically see it that way. Most street WC Swing dancers I talk to refuse to acknowledge the existence of a "basic step" at all, but if I push hard enough I can get them to admit that if there has to be step we call basic, it would most likely be either the Side Pass or Underarm Pass.
After collaborating with a few swing dancers on the matter, I understand that their concept of a syllabus is not necessarily to list steps in order of difficulty, starting with a perceived basic action like we do in ballroom. Instead, they think in terms of the order one might teach them in a beginning group class. And if you've ever been to a beginning WC Swing group class taught by a street swing dancer (not a ballroom teacher who knows some WC Swing), the first step you would learn would be the starter step to Throwout... Which is more or less an EC Swing basic followed by a Throwout, usually then followed by either a Sugarpush or a Side or Underarm Pass.
So to stay true to the Swing community, I have chosen to keep in step (no pun intended) with their concept of WC Swing syllabus, starting with the (1) Starter Step and (2) Throwout, then following with the basic "Passes" --(3) Left Side Pass, (4) Right Side Pass, and (5) Underarm Pass, and then finally arriving at the (6) Sugarpush.
A very knowledgeable person in matters of WC Swing is my very first Swing teacher from years back, Sonny Watson. He has a really good website dedicated to all forms of Swing,
http://www.streetswing.com. Since it's technically not my area of expertise, I always refer people to Sonny and his website for more information on the matter.
Regards,
Jonathan Atkinson
www.ballroomdancers.com