##Show them that you have nothing to hide.

This seems like it might be an issue of trust - or a lack thereof - between your parents and you. To be honest, their feelings are understandable. Families try to be open with one another, especially in the case of parents and children. When someone does something in what appears to be an attempt to shut themselves off from those they love, a little backlash is not unreasonable. (I recommend looking at [Too much computer?](https://parenting.stackexchange.com/q/26311/27638) on Parenting Stack Exchange to see how your parents might be thinking.) 

First and foremost, acknowledge that their concerns aren't fully unreasonable. I think I've said this here before, but in most disputes, the other party will be more agreeable if you let them know that you're not blindly disagreeing with them - because it appears that you are, in fact, disagreeing with them. I've had fights with my parents that probably could have been avoided if it was clear that each of us understood to a certain degree what the other was saying - we just disagreed.

Second, be open with them about what you were doing. I was a bit secretive of my activities when I first participated in Stack Exchange, in part because I had never even used social media before, let alone a question and answer site like this! I wasn't sure how much my parents would approve of my use of it. So I made the decision to hide it - not lying, but not keeping them informed.

Then the tsunami broke when my mom looked over my shoulder, and immediately got suspicious. Fortunately, I made what I think is your best choice: **I was open about what I was doing**. In particular, I did the following:

 - I explained what Stack Exchange was and how it worked.
 - I explained why I used it, and the benefits it had for me.
 - I reassured her that it was not interfering with other aspects of my life (such as homework).

I was honest, sincere, and completely open with my parents. I didn't hide *anything*, and they quickly understood that it made sense.

You have a similar case, and frankly, I think that's a good thing. You're not doing anything wrong; all you have to do is show them. Don't be afraid of doing so. You'll build trust, and in the long run, I think they'll respect your privacy quite a bit more.

##The conversation itself

Correct me if I'm wrong, but it seems like the typical conversation goes like this:
> **Parents:** Why close your door?

> **You:** I want some privacy.

> **Parents:** You are doing something bad that you want to hide.

Here's the point at which you quite literally prove them wrong. Here's a possible extension:

> **You:** I know that what I'm doing looks suspicious, and I understand your concerns.

> **Parents:** It looks *incredibly* suspicious.

> **You:** Well, here's what I'm doing. There this site called Stack Exchange. It's a question and answer site that covers a range of different topics. By participating, I'm helping people around the world.

> [Continue conversation as you wish.]

As NVZ pointed out, there's still the possibility of your parents further pushing the issue, i.e. saying "Why were you closing the door if you're doing something helpful?"

At this point, talking about privacy is a much better tactic. Bringing it up early in the discussion seems like a shield; it doesn't give that great a reason for you to have essentially hidden from your parents. They had no good reason to believe that you *weren't* doing something wrong, and that's probably why things have gone as poorly as they have.

However, you've now demonstrated what you've been doing, and talking about privacy no longer seems like just an excuse. It's a very reasonable justification, and I think they'll be more receptive to it.