My front wheel was steering to the right... now it's steering to the left. What's the cause of this?
Factors that have an impact on the steering include external forces and internal forces. External forces include things like cables, the riders centre of gravity and forces coming from the wheel (out of true, dead hub bearing). Internal forces have to do with the headset itself, if the bearing cups are not parallel, if the adjustment is incorrect, if a foreign object made its way into the headset, if there is pitting in the bearing cups. A bent steerer could also be it.

If you have eliminated the cable pulling (or pushing) as a problem, and your wheel is true, try adjusting the headset bearings. They should be as loose as possible without having any play or knocking. A dead bearing on one side of your hub would probably have a negligible contribution. If you've done that and it's still a problem, I would suspect the seating of the bearings not being parallel or the
 steerer tube not being perfectly straight.