If your spouse were trying to arrange a present, or hang out on fluther, or have innocent correspondences with members of the opposite sex, there would be no need to keep the existence of the account a secret. You just wouldn’t share the password. The fact that someone keeps the existence of the account a secret suggests to me that they are doing something they don’t even want me to guess is going on. The list of such things seems small to me, and most of the items on it are probably not good for a relationship.
Trust is based on behavior and transparency. Secrets are reasonable grounds for a reevaluation of the motives of the other person. Perhaps I’m colored by personal experience. I set up such an account to make sure that none of the emails ever resided on my computer. As it turned out, I hardly needed to have bothered. I turned myself in, and she is not interested in reading through the correspondence (which she can, any time she wants). Reading it will be painful for her, so she’s protecting herself, and lord knows I don’t deserve this, but she trusts that I will tell her everything she should know.
Now not everyone behaves like me, but I do know a number of other people who are very careful to maintain secrecy because they are doing things they really don’t want their spouse to find out. Now, I agree that we should trust, but I think we should also verify. In any case, when I decide to trust, it’s because of the behavior of a person. I pretty much ignore anything they say about themselves with regard to trustworthiness. Famous last words: “you can trust me.” I’ll never turn my back on someone who says that. I have no problem with someone who lives that.