I have the urge to not keep a secret.
Why don't you want to keep a secret?
I want to be an honest person. Honesty is the best policy.
There is a time and place for honesty and this is not the time and place. They trusted you with their secret, so you shouldn't talk about it with strangers. They may never trust you with anything and not just secrets.
I don't care, I may lose a friend, but at least I will always be true to myself.
I'm glad you value honesty so much, but you need to understand secret are met be kept secret. Sharing the secret is not going to be worth destroying your friendship.