Just to put a few theories to bed. 1. Captain only steering on almost all 737s. You go left because you can see the edge better and judge it. Simples.
Steering. I've had a couple of big birds in the nose gear and the cables and NWS still worked.
It is easy (especially for crew who've flown non Boeings before to inadvertently push TOGA when you want to disconnect the autothrottle. Happened countless times before over the years and will again. If you do it, a quick expletive and then press the disconnect before thrust rises and it's not a safety issue. Pulling back the levers and not disconnecting is another matter....