Another question about core sense amplifiers

On re-reading this, to ensure that I had fully extracted the content into my brain, I realized I didn't fully grok this. Could you expand a tiny bit on this (and especially the push-pull reference)? On thinking about it, I guess that what's happening is that there are two driver transistors, each attached to the center tap and one end, but with the polarity reversed. A positive pulse through one produces a positive pulse on the output secondary, whereas a positive pulse through the other produces a negative pulse on the output secondary. Or am I mis-understanding? What I don't get is why that's better than simply attaching two opposed transistors directly to the address lines, as one sees in the output stages of audio amplifiers, to handle the two halves of a sine wave. Noel