"We will conquer this wilderness. It will not consume us."
William tells his family the above after they were banished from their Puritan colony, condemned to live out their lives in the untamed wild for not following doctrine. This quote reflects William's high-mindedness, his arrogance, and his optimism. Part of the reason William chose to ignore the restrictions imposed on his family by their community is because he feels that his rules and his interpretation of religion is the best and most faithful and everyone else's is wrong. Ultimately, William's decisions cause everyone but Thomasin in his family -- including himself -- to die. They reflect his unwillingness to learn from his mistakes and do the right thing (and swallow his pride) for the betterment of his family. Fundamentally, he is a selfish man who only cares about his own happiness.
"Did ye make some unholy bond with that goat?"
William says this accusatory line to Thomasin, who he thinks has created a bond with Black Phillip, a goat the family owns that seemingly has incredible powers. William is naturally very untrustworthy of authority; he only realizes that Black Phillip may have had a hand in his family's demise when it is too late. Black Phillip is a powerful symbol of the Devil; his involvement in the family's affairs not only mean the family's end, but also reinforce their belief in God.
Especially because of how Thomasin is portrayed towards of the start of the film, this quote reflects the significant nature of her change. Initially, she is shown to be a kind and naive girl who would never scheme or do evil things. The quote reflects her father's surprise at her pact with the evil being. It also foreshadows Thomasin joining the witch’s coven.
