It can be said that Dimmesdale confessed in public because there was no other recourse for him. His body had become so physically weakened by the private "letter" that he wore and the shame that had built up in him. When he looked at Hester, he had something of a selfish envy for her, thinking that it must be better to at least be able to wear her guilt out for everyone to see rather than suffer in complete silence.
When Dimmesdale finally does confess, he is very close to death and is performing his final sermon. He finally stops relying on Hester—and by extension, their child—to carry all the weight and can at least die in a purified state. His spirit is finally strong enough to confess because his body is fading away, and he has little to lose. Despite what the townspeople may think of him, he does not want to face death so burdened with guilt.
Since the novel opened and Hester stood condemned in front of all the townspeople, Dimmesdale has longed to confess publicly to his part in...
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