Brown's journey into the forest is like a ritual. He feels he must undertake this journey to test his "faith." Brown is an absolutist. This means he believes that people are either inherently good or inherently evil. In this narrow-minded worldview, he comes to believe the latter, the people are inherently evil. He therefore loses his faith in humanity. He ceases being able to trust other people and this includes his wife. He loses his faith in Faith, so to speak.
Faith, on the other hand, is reluctant but accepts that Brown feels it is necessary to make the journey. In doing so, she symbolically accepts that each person must confront the human potential for evil. She is not an absolutist. She recognizes that people are capable of both good and evil and chooses to live life as well as possible.
Note that when Brown returns, he looks at her sadly and passes her without saying a word. She greets him with joy. For her, the dark journey into the forest is not something that should destroy their relationship. But Brown has lost faith in humanity and, as a consequence, he can no longer trust people. He can not trust Faith because he can't trust anyone anymore. Faith remains open to the possibility of a happy life. But Brown lets himself become psychologically melancholy. Being an absolutist, he lets his journey and confrontation of human evil cloud his mind with negativity. This negatively affects his relationships with everyone in his life.