Trust is essential in a relationship.
Privacy is a perfectly reasonable requirement in a relationship.
If having privacy means there's no trust, then there's really no relationship. If the only way someone trusts you is by you "proving" it over and over, then they don't actually trust you.
And if they don't trust you, that is going to turn into a very bad relationship soon, and very likely a controlling one as well, as they try to use control over you to substitute for their lack of trust/security. (I mean actually, it's already going to be a bad relationship, but the "bad" may not be fully showing itself yet.)
As to "nothing to hide" - I've always thought
this a pretty silly argument. I've nothing to hide about, for example, going to the toilet. Everyone does it, nothing shameful about it. And also, I don't want to broadcast it on the internet for everyone to see!!
Having your own boundaries about what you wish to share, wanting privacy and space which is just your own - these are perfectly reasonable needs, which a reasonable partner will respect.