how does the fellow traveler undermine goodman browns' faith?
One of the chief ways in in which the traveler undermines Young Goodman Brown's faith is by simply letting Young Goodman Brown undermine his faith for himself. At the outset of the tale, Brown leaves Salem village of his own volition, knowing full well that he is doing something he shouldn't be doing. Upon first leaving his wife, Faith, he thinks "Poor little Faith [...]What a wretch am I to leave her on such an errand!" Further, when Young Goodman Brown meets with the stranger in the woods, he quickly says
having kept covenant by meeting thee here, it is my purpose now to return whence I came. I have scruples touching the matter thou wot'st of.
Again Brown shows that he knows he shouldn't be doing whatever it is that he is doing. Although the traveler then encourages Goodman Brown to continue walking into the woods, Brown is never forced to do so.
Throughout the journey, the stranger only ever provides minor encouragement, at one point even telling Brown to turn back if he is so inclined. What the stranger does (seemingly) do is create apparitions of other people from Salem village, which is enough to stir Brown's own curiosity so that he decides to continue further into the woods. However, on numerous occasions Brown shows that he understands the journey is wrong; if he truly did not want to continue, he could turn back at any time. More importantly, he never had to leave on the journey in the first place. Brown's own curiosity and desire undermine his faith far more than any of the traveler's actions.
The traveler, the devil, shows Brown that humans have more in common with evil than with goodness. Notice how as Brown begins his journey, he believes he is destined for heaven. However, the farther the devil lures him into the woods, the more he undermines Brown's faith. Whether or not Brown's relatives really were in league with the devil is never clear, but the devil just plants enough seeds of doubt in Brown's mind to shake his faith, which he never really recovers, for he is never able to look at his fellow citizens of Salem the same ever again.
In fact, the devil so completely undermines Brown's faith that he reduces him to the most frightening presence in the woods, despite the devil himself and all those gathered at the black mass.
The companion, the devil in disguise, slowly chips away at his faith by revealing that the family and fiends that Brown knew were not what he thought. As Goodman Brown chides himself for taking this walk, the devil tells him that he has a long history with the Brown family.
Every person they encounter is acquainted with the devil . The way in which the devil reveals this information destroys Brown's faith. In the end, Brown realizes he never really knew any of them.