Actually, the pull stroke lets the saw teeth score the wood fibers more cleanly on crosscuts. It's like you're guiding the cut instead of forcing it, which really matters with tricky grain. I noticed on pine, where the growth rings are soft, pulling prevents the saw from jumping and tearing out chunks. Once you get the hang of that slow, steady pull, the edge is just glassy.
Ever try a pull stroke on plywood? The thin veneer layers can splinter like crazy if you push. A gentle pull with a sharp saw keeps that top layer intact. It feels weird at first, almost like you're not doing anything. But the cut ends up so clean you barely need to sand.