If you can't be trusted to keep your best friend's terrible secret, she's going to start thinking of you as traitorous, or completely unfaithful and unreliable.
A traitor is someone who betrays the trust another person has put in him, and the adjective traitorous describes this tendency. It is traitorous when a double agent sells her country's secrets to another government: and the traitorous person risks spending her life in prison or even being executed. It's also traitorous to tell your parents that your brother broke the kitchen window, if you've sworn to him that you'll keep his secret.