Is this story about an inward psychological journey where Goodman Brown discovers evil in himself but refuses to acknowledge it?
I respectfully disagree with the previous poster.
In my view, Young Goodman Brown does not exhibit the ability to confront the evil and hypocrisy around him and, for all his troubles, does not emerge any stronger or wiser at the end of the story.
Rather than confront the evil and hypocrisy around him, the title character hides from that very confrontation. See, for example, this instance of an encounter in the woods:
"Goodman Brown heard the tramp of horses along the road, and deemed it advisable to conceal himself within the verge of the forest, conscious of the guilty purpose that had brought him thither, though now so happily turned from it."
As I see the matter, at the end of the story Young Goodman Brown is much worse off than he was at the beginning. He has gained knowledge (e.g. he now knows that all humans, even the best of them, are not perfect), but he has failed to integrate that new knowledge into his world view and thus lives out the last of his days in despair and gloom.
Even in the certainty of evil all around, Young Goodman Brown fails to take any meaningful action. To his death, he continues to hide or pull back. When "the good old minister" passes by, what is Young Goodman Brown's reaction? "He shrank from the venerable saint, as if to avoid an anathema." And when he continues to share a bed with his wife? "Often, awaking suddenly at midnight, he shrank from the bosom of Faith..."
This protagonist in this story dies a defeated man, not a victorious one.
In "Young Goodman Brown," the protagonist, Goodman Brown, does embark on an "inward psychological journey," as well as a physical journey that is directly parallel to it. Yes, he does discover evil, or at least the potential for evil, within himself. However, I would not say that he refuses to acknowledge the evil within himself; in my opinion, it is far more accurate to say that Goodman Brown acknowledges the presence of evil or its possibility within himself, sonfronts it, and chooses to turn his back on it. In the story, Goodman Brown becomes aware of the evil of those around him and the power of its pull, but he refuses to give in to it and returns from his journey wiser and stronger in character.