As a linguist, I am interested in how people approach the question of what words mean, but I want to push back on this very common argument that one can base the meaning of the word on some kind of analysis of word structure or historical derivation. Generally speaking, this kind of argument is called an
etymological fallacy. Meanings are fully dependent on how people in a speech community conventionally use the word, and linguistic analysis depends on the active morphological processes that function in the language. So, although English has an active prefix "a-" and such prefixes derive originally from Greek or Latin, the initial syllable in "atheist" is not morphologically active, but vestigial. Typically, the active prefix is used to create new adjectives such as "asocial", "asexual", or "amoral", but not new nouns. In any case, the word "atheist" was borrowed from French originally, and most people who use it are unaware of its historical origins or usage. So it is misleading to argue that the prefix "a-" in this case means "without" or "lacking", since its stem is not even an adjective.
The other point I would make is that definitions should not be confused with meanings. Definitions are very succinct descriptions that help people discover a specific common usage, but words almost always have a range of meanings. That is, they are more or less ambiguous. So dictionaries often give several different usage definitions for a single word entry. Lexicographers tend to differ on how many word senses ought to be listed in the dictionary and how fine-grained those definitions should be. Sometimes, dictionaries have poor or misleading definitions, and I would argue that the word "atheist" tends to attract some rather poorly-worded definitions. I personally dislike the definition "person who does not believe that God or gods exist", because it is ambiguous between whether the person holds no opinion or holds an opinion that gods do not exist.
My preferred wording of the definition for the most common usage of "atheist" would be:
"Person who rejects belief in gods"
That is what most English speakers use the word to mean, but there are certainly valid usages for the one most favored by atheists in internet debates:
"Person who lacks belief in gods"
Why do most online atheists prefer the second definition over the first? IMO, it is because they usually engage in debates with theists, and they wish to use the most expansive definition that they can come up with--one that is easiest for atheists to defend. Nevertheless, it seems obvious to me that most people on Earth are theists and regard belief in gods as the default. Atheists reject the default. Hence, theists and atheists tend to get bogged down in arguments over which side most needs to justify their point of view.
