Recently, a friend of mine told me to mind what I say in my emails to him, even in jest. The injunction was not so much an admonishment for something I had said, as a warning against something I may say in the future. The reason: he had shared his email password with his girlfriend.
For some reason that freaks me out. I would never expect anyone I was in a relationship with to share their email password or bank pin with me unless it was a shared account or an emergency, in which case I would ask them to change it immediately after the emergency was over.
Of course, there are different ways of looking at everything, but everybody has some private spaces and should be allowed them. Having a personal space does not necessarily mean it is being misused. If I don’t want someone reading my messages, even a boyfriend, it does not mean I’m up to no good.
If my friend is fine with sharing his password, that’s his decision. But I don’t think by doing so the two are bringing any more openness into the relationship. Because he is going to watch what he says and he’s warned his friends too. So all that has been added is a layer of subterfuge.
I no longer feel comfortable mailing my friend. You may argue that since I’m not flirting with him or bitching about his girl or something like that in the mail, I have nothing to hide and the fact that she reads the mails shouldn’t bother me. But it does.

The issue, like you rightly pointed out, is not about trust. Its about privacy. The reason why I want to keep my communications private is not that its sensitive. It is so because my communications are nobody else’s business. Sometimes, not even my significant other’s.

In a more philosophical sense, your email is your identity online, its a means of authenticating yourself to whoever you are communicating with. Now by allowing someone else access to your email, you are compromising that identity (and not necessarily to the other party’s knowledge).
If you and your significant other would like to blur your identity boundaries, then that’s your decision. However, it is also your responsibility to ensure that this fact is communicated to everyone who is communicating with that email/identity.

Personally, I would like to know who the email is coming from. I don’t want to have to guess or verify if it was my friend or his/her significant other who sent that email.

Additionally, there is a very real threat of misuse. If you are in a relationship, then you are bound to have fights, misunderstandings. You dont want someone who is emotionally charged against you to have access to your email accounts and your communications. That is just asking for trouble.