Maybe you were in the right by law but I agree with the women there lives were in your hands . Ive never took a Uber ride but if I did I would want a driver with more common sense & logic. Although the other car was wrong for cutting you off just to exercise caution you could have slowed down as soon as you seen them put their turn signal on.You had at least a car length of time but instead you speed up which put everyone's safety at risk.