Chaos theory: bfly flaps wings in NYC causes typhoon in Tokyo. So 1 little sin in the beginning escalate to sin & suffering for all mankind?

Not at all like the butterfly, it works its magic by random chance and that is also what mostly cause the typhoon.

The "one little sin" story is about how god cannot overlook the least disobedience. He MUST punish, punish, punish, whenever people do not do what he had planned. Today we mostly call that kind of person a 'contol freak', but there are just as many of them today as there was in biblical times. I suppose that is what keeps the story popular :(

So instead of the butterfly, remember Shakespeare, "Much ado about nothing".