How does thie quote "Nothing can bring you peace but yourself" relate to the idea that "it often takes courage to defend our own view of the world?"
Most of our time is spent alone with ourselves in our minds. We do spend a lot of time with other people, but whenever we are not actively talking or listening to someone our thoughts dominate our consciousness. What this means is that our attitudes towards ourselves will be very important because negative emotions towards ourselves will intrude on our thoughts and deny us peace.
Therefore, we need to be true to ourselves and to defend our view of the world. If we do not do that, we may be more accepted by other people, but we will not feel good about ourselves. We will feel that we are betraying who we are and that will hound us. We will never find peace if that is the case.