What does it actually mean to call yourself an atheist?

It depends how broadly you use the word. In its broadest sense, atheism is simply an absence of belief in deities. Less broadly, it is a rejection of the belief that any deities exist, and in the narrowest sense it is the specific position that there are no deities at all. Philosophers mark the difference with labels: "implicit" atheism is lacking theistic belief without consciously rejecting it, while "explicit" atheism is a conscious rejection, and it is usual to define atheism in that explicit sense. Antony Flew and Michael Martin add another pair: "positive" atheism affirms that gods do not exist, while "negative" atheism covers every other form of non-theism.

The broad sense leads somewhere surprising. In 1772 Baron d'Holbach wrote that "all children are born Atheists; they have no idea of God", and the writer George H. Smith argued that even a child able to grasp the question, but still unaware of it, would count.

The label has always been contested. Ancient Romans accused Christians of atheism for not worshipping the pagan gods. In Athens, the poet Diagoras of Melos was sentenced to death as a "godless person" after mocking the Eleusinian Mysteries, and fled. Socrates, portrayed in Aristophanes' comedy The Clouds as teaching that the traditional gods don't exist, was later tried and executed for not believing in the gods of the state, a charge of atheism he vehemently denied. The historian David Sedley found that no 5th-century BCE philosopher openly defended radical atheism, yet radical atheist ideas are clearly attested, so Athens probably had an "atheist underground".