Accepting being Wrong

I have always prided myself on being firm in my opinions and having an opinion about everything. But lately I have been put up to question opinions I have declared. There are few things where I am actually torn on how I believe, most things I am very set in my ways. I am having trouble dealing with two right answers or being able to be two opposing forces at once. I just want to help and really I want to help women, because that is what I do. She is making me realize this more and more. And frankly she has been making me realize how wrong I have been and how big my blinders were. Because as she put it, would I hate her and judge her for doing the same kind of thing? Probably not. And what if I was to do the same sort of thing one day? So why would I have one set of rules for her or myself and another for everyone else?