You're not an atheist
There are various ways religious people try to dismiss atheists by claiming that they're not actually atheists. The most common argument I've heard is, "You can't know that a god doesn't exist," or the similarly worded, "you can't prove that a god doesn't exist." The argument then follows, if a person can't know is a god doesn't exist, then they're not really an atheist, but rather an agnostic. Another way of putting this argument is to say that atheists are merely "professing" atheists.
- P1. Only those who can prove that a god doesn't exist can be an atheist.
- P2. It's impossible to prove that a god doesn't exist.
- C1. Therefore, nobody can be an atheist.
The first problem is the equivocation fallacy in P1. The definition of "atheism" is baked into the word itself, a meaning "without," theism meaning "belief in a god." Thus, anyone who isn't a theist, is an atheist by default, or, in basic English, unless you believe in a god, you're an atheist. There are atheists who do claim to know that a god doesn't exist, they're called gnostic (or strong) atheists. However, most atheists I know admit they can't prove some definitions of gods don't exist, and are therefore agnostic (or weak) atheists to those gods. There are also people who haven't considered the existence of god and are therefore atheist by default, these people are known as implicit atheists.
One way I find that helps explain the problem with this argument that doesn't involve trying to teach someone the various categories of atheism is to use their own religion as an example. For example, let's say an Evangelical Christian says you're not a real atheist because you can't prove that his god doesn't exist. Respond with something like, "That's like saying, 'you're not a real Christian because you don't follow the Pope.' This allows you to have the argument about who gets to decide what it means to be in a group. Should the group get to decide, or should outsiders get to decide?
Some Gods Can Be Disproved
P2 asserts that you can't prove that something doesn't exist, but, in fact, you can. Anything that is defined as a logical impossibility cannot exist. For example, a square triangle is impossible and cannot exist, a one gallon jug that can hold ten gallons of water cannot exist, and so forth. The same is true for gods that are defined in contradictions. If someone claims a god exists that is both perfectly good all the time, and perfectly evil all the time, we know that such a god can not exist. Sometimes religious people define their god using logical contradictions. When they do, it means the god they have described cannot exist.