Remarkably, and possibly for the first time, I disagree with
@benphyr ...
Sure, the largest force is exerted by the feet, but I don't think that's what we mean by "pushing". What other way is there to make the bike go?
The relevant distinction between pushing and pulling is really the difference between our bikes and traditional recumbents (TR).
On a TR you
only get power like a leg press machine: between the seat back cupping your lower back and the pedals. That's pushing.
On a CB, we have another way to exert force on the pedals: between the handlebars ("pulling") and the feet. A CB can be ridden without a seat back ... Try this by inching your butt forward a bit and using your hands to pull your upper back off the seat. It's easy. Pure pulling.
That's "pulling" taken to the extreme. It's optional: a CB can be ridden with only pushing like a TR ... that's what riding no-hands is.
But pulling is really our advantage over TRs. It's our ability to engage the upper body that makes our bikes faster, especially uphill. It's much closer to a rowing machine than a leg press machine. I find myself doing this engagement whenever I'm working hard: uphill, digging in to make a traffic light, late to work, trying to catch someone in the bike trail, (escaping from a dog!). In those situations my arms are pulling my upper back away from the seat as I'm giving maximum pressure on the pedals.
As I said above, it's optional; we get to mix it up. I think we use pulling when we want more power, but relax and ride partly like a TR (" pushing") when we're just cruising.
That's my experience: 10 years on TRs, 9 on my various Q model CBs.