For many people, it can be difficult to "out" themselves as an atheist or even an agnostic. Friends, family, coworkers, or total strangers may all have a variety of negative reactions which can range from accusations to simply refusing to accept it. In many cases, these reactions come from people who just don't understand atheism and have formed a poor conception of disbelievers as a result. If you're having a tough time explaining to someone why you don't believe in god, here are three suggestions of ways you can gently try to remove the mistaken notions they have about it.
1. Atheism isn't really a belief system of its own.
A lot of people assume, as soon as you tell them you don't believe in god, that you must therefore believe certain other things. They may jump to the conclusion that you think their own religious beliefs are immoral or stupid, associate you with certain political and moral attitudes that you don't really hold, or think that you believe the existence of gods is completely disproved or utterly impossible.
One way to try to counter these notions is to point out what the word "atheism" literally means. Essentially, the "a" prefix means a lack of, and "theism" means belief in god. So, you might point out, the fact that you are an atheist doesn't say anything about what you actually do believe. It only means that the arguments for god's existence are not convincing to you, so you don't accept it. In other words, it's a common misconception that atheists are people who believe there is no god - the truth is that atheists are people who don't believe in god.
The distinction between these two ideas can sometimes be lost on people. They may say it sounds like you're actually an agnostic, not an atheist. That is because there is actually less difference between these terms than many people realize. An agnostic is a person who is not convinced either way on a subject, and it may be that many atheists can also be defined this way. In popular use, an agnostic is often understood to find some strengths in both sides of an argument and to be indecisive for that reason.
This isn't what the term technically means, but it can be a helpful way to use it, and you can use this to explain why you consider yourself an atheist rather than agnostic. In some cases, however, you may wish to accept letting someone regard you as an agnostic if it makes them feel better about your lack of belief. Most atheists argue that the likelihood of a god existing is so low that they are quite certain there isn't one, but few will argue it can ever be proved that there is no god - so in the truest sense of the word, it's often accurate.
2. Atheists can still have moral values.
There are a lot of arguments in philosophy about morality and why people have the moral values that they do. They can go a long way towards explaining why people who don't believe in a god still tend to have moral values. Unfortunately, most of these arguments are too big and complex for a discussion with someone who's already misunderstanding you. You need a simple way of explaining why you still want to be a good person even if there is no heaven or hell.
In many cases, the best way to go about this is to appeal to your emotional connection to the person you're speaking with. If you are talking to a friend or family member, you can point out that even if you don't believe in a god, it doesn't change any of the reasons why you care about them - the experiences the two of you have shared, your familiarity, and all of the things you love and admire about them. Being an atheist doesn't suddenly make you lose regard for the well-being of those around you, because you still have the same emotions and social inclinations any other human being would.
Another effective answer that can be added to the first one, or used by itself with someone you're not as close to, is an appeal to the values expressed by many religions without the supernatural punishment and reward aspects. All religions have some form of the golden rule in their teachings: "Treat other people as you want to be treated." Ask them if this moral advice makes any less sense if it is not attached to a religion, and they will probably admit that it still makes good sense. Like everyone else, most atheists want to be treated fairly and respectfully because otherwise life can be difficult and unpleasant. So, they will treat others this way and hope for the same in return.
3. Atheists are not trying to destroy religion.
There are some well-known atheists who have made public arguments that religion does more harm than good and that people should stop believing. The most well-known example is probably Richard Dawkins, who has written extensively not just about why he does not believe in god, but also why he thinks religion hurts society.
Because Dawkins and others with similar beliefs have attracted so much attention and sold so many books, many religious people are given the impression that atheism is an organized movement with an agenda. But, since you've already established that being an atheist doesn't say anything about what you actually do believe, you should be able to explain here that no one atheist, or organized group of atheists, speaks for atheists as a whole. Atheism isn't a belief about the direction society should go in or what's right and wrong, so there is no atheist agenda to destroy religion - or to do anything else, for that matter.
Hopefully, this will be enough to convince family and friends that although you don't share their beliefs, you don't look down on them and are not going to try to change them. Most people will feel much more comfortable if they have the sense that your beliefs are just different from theirs, rather than being in opposition to them.
Unfortunately, the sad truth is that not everyone is ready to accept atheism. There are still people in the world who will respond to unbelief with hostility, and it won't matter what you say to them because they have already made up their minds. But family members and long time friends, in most cases, will be willing to accept your outlook once their misconceptions have been corrected. With patience and well-spoken arguments, you can safely reveal that you don't believe in god to anyone who is willing to listen.