According to chapter 11, "The Interior of a Heart," Dimmesdale was more than once in want of telling the congregation that he was, indeed, a hypocrite. In a lighter view of Dimmesdale, he is actually described as someone who would naturally have preferred to lead a life of truth, but that he was way too venerated, way too admired, and way too blindly followed by his flock. It would be shocking to them, a tragedy indeed, to learn that their young, godly man was a big sinner.
Dimmesdale tells an approximate of the truth when he admits to the flock that he has sinned just like them. However, the crowd is way too fanaticized by the pastor to take his word at face value.
He had told his hearers that he was altogether vile, a viler companion of the vilest, the worst of sinners, an abomination, a thing of unimaginable iniquity; and that the only wonder was, that they did not see his wretched body shrivelled up before their eyes, by the burning wrath of the Almighty! Could there be plainer speech than this? [...] Not so, indeed! They heard it all, and did but reverence him the more. [...] “The godly youth!” said they among themselves.
The same thing will happen eventually in the end when, even after a full confession, the villagers will pick and choose what to remember about what the priest says, and even they even talk of the event as one of supernatural nature.
Essentially, it all comes down to simple cowardice. Why not just say "I was the man who impregnated Hester Prynne, the woman you all hate so much." It is hard to even fathom it. He has built such a strong repute in this village that the idea of undoing all of it is unthinkable.
Keep in mind that this is also very telling about Dimmesdale's true feelings for Hester. Has history not shown us what a man in love is capable of doing? Men have created wars, battled empires, gone broke, or have voluntarily lost their dignity for the sake of women for ages. Why didn't Dimmesdale take that step on behalf of his love for Hester? Because there was very little love for her, or her daughter, to sacrifice everything for them. This is not expressed verbatim in the novel, but there is a lot to infer from Arthur's other behaviors to conclude this.