Sharon asks (with my answer interspersed:)
If a person does not believe in God, therefore without even using the term God, how does an atheist explain what “sin” is? Does it even exist in your view?
“Sin” as commonly understood is a theological concept. Non-theists such as myself do not subscribe to such concepts. Therefore, we can only really explain it in terms of what theists say it is.
If it is related to morality? Who defines that?
If you as a theist define morality as “whatever you think God wants you to do,” then “sin” is falling short of that in any way — including (for example) failing to obey a command to destroy an enemy tribe including women and children, or refusal to strap on a suicide bomb.
From a non-theist point of view, morality (“ethics”) is a the set of principles that guides an individual’s actions with respect to others. It is not a fixed code, but a set of personal principles. Societies work because the majority of their members can broadly agree on ethical codes, but such codes can vary substantially from society to society, and there are always some percentage of overt or covert non-conformance within societies. Probably the single most subscribed-to ethical code is some variant of the Golden Rule.
Why is it that all individuals whether we call it sin or morals all seem to go against them?
Because ethics is not as simple as high-handed moralists would have you believe. The picture they paint of morality is actually a cartoonish oversimplification of the ethical considerations mature individuals need. In applying a well-developed ethical system, there are always considerations about trade-offs and cost-benefit analyses. “Doing the right thing” from one perspective can simultaneously be “doing the wrong thing” from another— this is to be expected in some cases, and there is no codified ethical system that covers every case. Ultimately it is the individual who decides, and who must live with the consequences— to themselves and others.