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Logic and rhetoric
The argumentum ad iram fallacy (ad iram, Latin for "to anger") is an informal logical fallacy, that involves accusing one's opponent of being angry or holding their beliefs for anger-related reasons, which purportedly disproves their argument or diminishes its weight.
P1: Person A says P.
P2: Person A hates P and/or Q.
C1: P is false.
One can easily see the problem here. The atheist does not believe in the deity in question; thus, they cannot hate what they don't believe in (that would be misotheism, not atheism). Also, the atheist could have any reason not to believe in said god; their emotional state doesn't invalidate their claim.
It is also an ad hominem attack and strawman argument that appears often on the Internet; e.g., a person disagrees on a political issue, and one side accuses the other of "being butthurt" and "crying like a little baby", even when no emotion was exhibited by the accused. It also applies to the idea that, if a person doesn't agree with a system they should "get out" and find a country that agrees with a strawman idea of what the dissenter believes, e.g. "Go back to Russia!".