There is nothing lost in apologizing. It makes us realize how important the other person in our life is and that we are willing to give up any thing to make them happy. Even after that they don't realize and be stubborn we can't change them but we can change ourselves to be a better person.
I'm a very stubborn person but When I'm wrong I will tell you or if I've wronged someone and didn't mean to Or even realized I did I will tell you I'm sorry that's just how I am. I know not everyone's going to like or respect you but if I'm wrong I will say I'm wrong regardless of the situation!!