It could be that the AI is cunning enough to make its attacking unit turn to face a new direction, during the engagement (but when I try re-orienting a spear unit to trap a king/general but the spears are fighting, the order usually gets ignored) and your spears are merely responding to this.

If not that, then maybe a second unit was pushing at the gap between it and the next line unit, so the assymetric push forced your spears to turn. Sounds like a useful tactic to try for ourselves...

One occasion, I have had units in holdform/holdpos which actually chased a unit they routed. I was annoyed because more was coming at me but left them to their own devices. After about 100 yds, they broke off pursuit, turned around and returned to their original station. Holdpos therefore has a certain amount of flexibility to it (they're not totally rooted to the spot) and perhaps morale getting up to impetuous levels will trigger them to chase routers, but not too far.