Sin is a religious term for the violation of a religious or divine law. These sometimes overlap with moral and ethical rules. For example the 6th commandment, "Thou Shalt Not Kill," is generally considered a moral rule; however, Deuteronomy 14:21 states, "Thou shalt not seethe a kid in his mother's milk" has no modern ethical or moral ramifications. Often times the suggested punishment for sin is itself immoral. For example, Leviticus 20:13 suggests a punishment of death for homosexual acts. Various punishments exist for planting different crops in the same field, wearing cloth of multiple fibers, and eating shellfish, among others, which are sins but have nothing to do with morality.
Since atheists do not believe in God, it is meaningless to accuse an atheist of being a sinner (or to threaten them with the purported consequences of being a sinner). Humanistic atheists recognize the concept of right and wrong actions in terms of their impact on other people, but the idea of sin is basically irrelevant without appealing to a deity.
The declarations of sins by God invariably travels through some medium, such as a book or a pastor. This inevitably makes the concept of sin subjective and completely disconnected from human and animal suffering. Even if one ignores this problem, sin is then subject to the whims of a deity who may say that killing is wrong or that killing is required as punishment for picking up sticks. The Euthyphro dilemma suggests that this subjectivity means that sin is disconnected from morality.
Since the concept of what is a sin and what isn't changes with the religion (and even with the denomination), sin is an example of the religion inventing a problem and then selling a solution.
Sinning undermines claim of belief in God
"No one believing, as the laws prescribe, in the existence of the gods has ever yet performed an impious action willingly, or uttered a lawless word. Anyone acting in such a way is in one of three conditions: either, first, he does not believe the proposition aforesaid; or, second, he believes that though the gods exist they have no concern about men; or, third, he believes that they can easily be won over by the bribery of prayer and sacrifice"
- — Plato, The Laws