This act discourages his confidence to a great degree. Right there he starts to doubt his confidence and starts to have doubts on this quest.
It is obvious that the devil himself planned for Goodman Brown to meet the old catechism teacher. He planned this because at this point the Devil agrees with him and tells him to turn back to prevent that Faith should come to any harm like the old woman in front of them on the path. (The old woman being his teacher).
Goodman Brown's faith is harmed because the woman on the path is the woman who taught him his catechism in youth, and was still his moral and spiritual adviser. .
The Devil and the woman talk and afterward, Brown continues to walk on with the Devil in the disbelief of what he had just witnessed. He blames the woman for consorting with the Devil but his own pride stops him from realizing that his faults are the same as the woman's, for he is consorting and interacting with the devil.
Goodman Brown almost immediately declares that he kept his meeting with the Devil and no longer wishes to continue on his errand with the Devil. He says that he comes from a "race of honest men and good Christians" and that his father had never gone on this errand and nor will he. The Devil is quick to point out however that he was with his father and grandfather when they were beating a woman or burning an Indian village. These acts are ironic in that they were bad deeds done in the name of good, and it shows that he does not come from "good Christians." .
Here is a controversial point, as no one knows if this was true if the Devil was telling the truth, but what matters is that the Devil purposely brought this up to confuse and corrupt Brown.
Thinking he has won and his sense of pride taking over again, he feels proud considering he has resisted the devil while his teacher couldn't and cannot wait to be in the arms of Faith. Once again, he has realised that he no longer needs this quest and wishes to be back and one with faith.