I get what you are saying about the word sin. I used it partially just to be polemic, although I do like the more personal connotations of sin versus abstract notions like morality.
Sin is an overloaded word. It can mean a general concept "Murder is a Sin" - and that matches up nicely with saying "Murder is immoral".
But sin also is used as a verb "I feel bad when I sin". I guess you could say "I feel bad when I am immoral".
And finally, sin can refer to a specific instance of immoral behavior, "I feel bad for that sin I committed last Tuesday". That tends to work better than "I feel bad for the moral transgression I committed last Tuesday:
I see and then I agree. I guess the word that you used the threw me off into a tangent was actually "believe", no just "sin".
I absolutely agree that using the word "sin" instead of the phrases "immoral act" or "moral transgression" has practical value. The thing is I do think that the word is really overloaded with religious concepts and dogmatism and reclaiming it for secular purposes with an altered usage would be really hard. Despite that I do see the utility in trying to do so now.