I can keep my atheism to myself. In fact, I usually do. Most casual acquaintances do not know that I am an atheist because I've never told them. Some of my co-workers know because I stupidly confided in one during a moment of weakness outside of work, and she found it sufficiently interesting to tell anyone who would listen. But it isn't like I've ever said anything at work that would lead anyone to suspect I was an atheist. My immediate family knows; some of what little extended family I have left does not.
Now that we've established that I can keep my atheism to myself, it is time to explore the far more interesting question of why I don't always keep my atheism to myself. And here, we have to look no further than the fact that I am surrounded by evangelical fundamentalist Christians who refuse to keep their religious beliefs to themselves. Of course, what I just said is a massive understatement. The problem is not that these evangelical fundamentalist Christians do not keep their beliefs to themselves; it is that they use every opportunity to promote their religious beliefs, even when it is clearly inappropriate to do so.
Most human communication involves some give-and-take. When someone I am meeting for the first time goes on and on about the kind of movies he likes, I am liable to mention what kind of movies I like. It is part of the normal conversational flow. As we get to know each other, we disclose things about ourselves as a way of seeing what we might have in common. If the evangelical fundamentalist Christian is going to insist on going on and on about his or her religious beliefs, I am likely to at least mention that I do not share them. I am even more likely to mention that I do not share them if I feel that they are being pushed on me in an unacceptable manner.
Ultimately, I'd be happy to keep my atheism to myself so long as religious believers kept their religious beliefs to themselves and stopped trying to impose them on others through legislation or social pressure. Atheism will always be here because there will always be at least a few people who do not believe in gods. I don't expect to see that change. What I would love to see change is for atheist/secular activism to fade away due to becoming thoroughly irrelevant. If there were no church-state violations, there would be little need for anything like atheist or secular activism. If religious believers weren't pushing their beliefs, none of this would be needed and it would go away. I think that would be great.
Religious believers have the power to end atheist/secular activism, and I wish they would do so. By keeping their religious beliefs to themselves instead of pushing them on others and refraining from legislating them, they could make talking about atheism irrelevant. But as long as religious proselytizing is a thing, atheists are going to keep expressing ourselves. And as long as church-state violations occur, secular activists are going to keep pushing back.