Simple reasoning probabaly won't help you overcome your fears. Just because your brain says "No" your emotions say "Go" and guess who wins? You can change the bad habit of being afraid by developing a new one. Let go of fear. Even when you don't feel it, convince yourself that you will not let that fear get the best of you. You must think differently on purpose. After awhile, your new attitude becomes habit.
“You gain strength, courage and confidence by every experience in which you really stop to look fear in the face. You are able to say to yourself, ‘I have lived through this horror. I can take the next thing that comes along.’ You must do the thing you think you cannot do.”