Her decision to stay and wear the letter A openly on the chest is not a passive acceptance of the punishment, not even an admission of guilt—for she feels no shame for her transgression. It is a quiet defiance—she chooses to stay and bear it, instead of being driven away in humiliation. When the town decide she can remove the letter, she responds:
“"It lies not in the pleasure of the magistrates to take off the badge," calmly replied Hester. "Were I worthy to be quit of it, it would fall away of its own nature, or be transformed into something that should speak a different purport."” (Ch.14)She doesn’t need their mercy or their forgiveness, because she doesn’t accept their charges in the 1st place. As Hester lives in solitude, away from society, she changes and grows, and no longer accepts the social rules—their moral codes mean nothing to her. In a way, she is freed.
Arthur Dimmesdale, in contrast, can never be freed, except by death. He is too weak-willed and cowardly, too afraid of public exposure, with too much to lose. He may not be punished by the town, but he has his own kind of punishment, because of guilt and a keen awareness of his own hypocrisy and deceit. It is amusing that he is aware of his own hypocrisy, but doesn’t realise that his worst deed is not the fornication, but the fact that he leaves Hester (and their child) to be punished alone.
Hester and Arthur “commit the same sin”, but they view it very differently, and afterwards live with it differently.
The Scarlet Letter is a great book. I’ve finished reading it. Despite ideas floating around in popular culture, The Scarlet Letter is not an adultery novel. It’s not about sin either—less about sin than about the concept and idea of sin. Himadri would agree with the narrator that it’s a tale of human frailty and sorrow. I don’t disagree, but I think it is, above all, a book about symbolism and the (stupid) meanings that people attach to it.