I understand your need for privacy and your own space. I am the same way. I don't like anyone knowing about many things I do daily, especially online. It's not that it's anything I'd be particularly embarrassed or ashamed about, it's just that I highly value my own personal activity without the eyes of anyone else watching or knowing what I am doing. It's usually not dependent upon what I am doing that makes me want to be private, it's just the principle that I feel like I have more personal space and freedom if I can have things I do that no one else knows about.

But I also understand his suspicion. It would seem shady if my guy turned away his computer screen whenever I entered the room.

I think you need to be firm with what level of privacy you want and draw specific boundaries for yourself that you'd like him to respect. If there is a healthy level of trust in the relationship, it shouldn't be a problem. If there has been trust issues, you might want to work those out before you explain how much privacy you'd ideally like to have.