I find some people's persistence in this matter to be amusing. Asymmetrical means something lacks symmetry. Apolitical means someone abstains from politics. Asymptomatic means without symptoms.
But atheist, rather than the obvious 'without theism', simply HAS to mean more than that, because......reasons.
The persistence of this 'proof' is quite amusing as it has (at least) 2 very basic flaws.
1) There is no rational reason that the word should be considered a-theism (without belief in gods) rather than athe-ism (the doctrine or belief in being without gods). If we go the 'meaning comes from the letters' route than it still gives you no reason to prefer one definition over the other.
2) Much more importantly, as it relates to the fundamentals of language an communication, you cannot definitively derive the meaning of a word either from the letters which make it up
or the knowledge of the meaning of a completely different word (theism, apolitical, etc.).
While it is true that knowledge of prefixes and suffixes can help you to guess the meaning of unfamiliar words, these rules do not necessarily hold true in all cases.
For example anti-hero and inflammable do not follow the expectations of the prefixes they contain. Moreover, we can't tell simply from the letters whether or not a word is actually contains a prefix or a suffix. Aback doesn't mean without a back and prism isn't a doctrine or belief in PR.
The only way you can know this is to know the actual meaning of the word in the first place, which comes from convention and its usage in context. Words also don't have meaning in isolation, they gain their meaning from the other words around them and the situation they are used in. When ibn Taymiyya refers to Avicenna as an atheist I know this is different from referring to Richard Dawkins as an atheist.
Language is use of language, and everything else is hot air (which differs from the hot air of a balloon).