Howmight the man with the staff whom Young Goodman Brown meets in the woods equate with a Freudian psycholanalyst?
This is a great question.
The detail in your question ("the man with the staff") makes me think of the famous photographs of Freud with his cigar (see the second source for one such image). Both staff and cigar serve as a characterizing feature somehow and suggest a sort of phallic authority or mastery or, at the very least, a tool of self-discovery. The man with the staff in Hawthorne's story, after all, makes a second walking stick out of a maple branch and tosses it to Young Goodman Brown before letting him travel alone in the woods.
The goal of classical psychotherapy is (in my limited understanding) to bring the patient through an inner journey that leads to healing and integration. Freudian psychotherapy also focuses on what many people might consider the baser side of human existence, including sexual and bestial drives as well as bodily functions that we normally don't talk much about. In this regard, at least, the story does resemble a psychotherapy session. The analyst guides the patient down dark and forbidden pathways, overcomes resistance of the patient, makes creative use of the patient's transference (the man with the walking stick, early in their meeting, seems to resemble Young Goodman Brown's father), and so on.
If you are writing an essay on this topic, read up on Freudian psychoanalysis. Also, consider making use of Freud's famous assertion at the celebration of his seventieth birthday: "The poets and philosophers before me discovered the unconscious."