While this event was not in response to a TCAS TA or RA as commercial pilots we receive a considerable amount of training in collision avoidance. The focus is in the vertical. Primarily because TCAS doesn't , as yet, coordinate turning manuevers.
It is also worthy of note that the turning radius while in the cruise phase is measured in nautical miles.
Hopefully, that will give some explanation as to why we dont simply break right.