If you don't believe in any gods, you're an atheist — but not everyone who doesn't believe in gods wants to be called an atheist. Some object to being labeled an atheist and to identifying as an atheist if though the term accurately applies to them. Is that justified or reasonable? Are there good reasons to refuse to identify as an atheist?
The most common reason given for rejecting the label 'atheist' is the idea that there is something wrong or inappropriate about identifying yourself by something you reject or by something you don't believe. After all, no one calls themselves a non-astrologist or non-elf-believer.
Identity and Labels
The first problem with this argument is that it seems to presume that accepting the accuracy of a label means that this label somehow creates or forms an identity for a person. This premise simply isn't true — not every label is an identity and not every label plays much of a role in making up our identity.
For every person, there are dozens and perhaps hundreds of possible labels that might accurately apply to them — and for every label that doesn't apply, it's opposite will apply. This doesn't mean that this label has to be meaningful for them or play much of a role in how they think of themselves.
Every resident of the state of Virginia is a Virginian; everyone else is a non-Virginian. Everyone who hasn't had sexual intercourse is a virgin; everyone who has is a non-virgin. Everyone with one particular configuration of sexual organs is legally a male; everyone with a different configuration is legally a female.
Some of the people to whom these labels apply care about that fact a great deal; for others, it's irrelevant. Some of the people accurately described by these labels care enough that they actively identify themselves with them; others don't give it a second thought. None of this changes whether the labels are accurate or not — the meaningfulness of the label to a person is a personal choice; the accuracy of the label is a matter of empirical facts and definitions.
Identity and Non-Belief
The second problem with the above argument is the false equivalency being drawn between not believing in gods and not believing other things like astrology. In principle, perhaps they all should be equivalent and perhaps disbelief in gods should be treated as no different than disbelief in other supernatural and mythological things.
That might be the ideal, but the fact is we don't live in an ideal world, do we? We live in a world where belief in gods has been so important for so many people for such a long time that we have a special word for it and also have a special word for those who don't join in. We don't have a special word for most other beliefs and we don't have a special for word for any other cases of not believing.
To refuse to accept and deal with that fact is to refuse to deal with and accept reality — just the sort of thing which many atheists accuse theists of doing. Wishing that belief in gods were treated the same as belief in elves or fairies won't make it so. Even if society changes to the point where such beliefs are generally treated the same, that won't change the long course of human history in which they weren't treated the same and during which special terms were created to describe belief and disbelief in gods.
What's more, there are plenty of cases where people have happily identified themselves according to what they don't believe and/or oppose. Countless numbers have described themselves as anti-communist or anti-capitalist, anti-imperialist or anti-war, anti-defamation or anti-racist, and so forth. Was there something wrong with them? If not, then how can there be something wrong with calling yourself an atheist or an anti-theist?
Honesty and Anti-Atheist Bigotry
Let's ignore all of this, though, and consider the reasons why this argument is being made at all. It seems implausible at best that people objecting to the label "atheist" are actually doing so for the reasons that they profess. There's something else at work here.
You can tell by considering the example of astrology. There's no special word in English for people who don't believe in astrology or who criticize astrology, but we can of course create such terms: non-astrologist and anti-astrologist. These are not common labels, but they accurately apply to some people. Can you, however, imagine anyone objecting to those labels being used to describe them in the same way that some people object to the label "atheist" being used?
It would be perfectly legitimate for a person to insist that their not believing in astrology isn't important enough for them to go around introducing themselves as a non-astrologist. That is, in fact, how most non-astrologists handle it and it's how most people handle all the other things they don't happen to believe. That's because most of those beliefs don't have enough social, cultural, or political importance to bother mentioning at all, regardless of whether they do or do not believe.
But theism and atheism are different because the belief in a god or gods has a great deal more social, cultural, and political importance than astrology, elves, fairies, or anything else that's similar. That's also the real reason why people object to being labeled as an atheist even when the term is clearly accurate: they don't want to be associated with a distrusted, despised minority.
That's not entirely unreasonable because of all the animus, bigotry, and discrimination that is directed at atheists. What is unreasonable, however, is to refuse to acknowledge all of this and to pretend that one is somehow taking a high road by treating the entire question as unimportant or irrelevant.