1) When he says "Pull" - he doesn't state what direction you are pulling into...If the direction she's facing is 90 degrees to his and he is sending his hand forward/backward (in relation to the direction he is facing), then I can see how what he calls: "pull and push" looks to us like her hands are being swung from side to side...
In BR latin, we also operated with terms pull and push, however it was about force developed in connection as result of leader moving close towards follower (push) or away of her (pull), where arms act like a kind of spring, and force is more or less parallel with the line connecting center of leader and follower. Some were using more pull, some more push and the trends were changing along timeline ... but anyway, push/pull wasn't about leader standing still and moving furniture from left to right side (and even if you are moving furniture, you won't do it that way but will usually try to lean towards or away from the furniture to make it move). However, many social dancers looking that got similar wrong ideas ... and teaching that way produces even more traffic cop leaders combined with furniture followers that are never in balance because guys are always pulling and pushing them out of balance, that don't look like they are dancing but like "being danced". But on the other side, it can partially replace going to gym, so maybe it's not that bad either
2) Perhaps this habit was born (and spread) from misconception of this: