John Proctor has lost everything, but the one thing he has left is his good name, his reputation. As John says himself, he's already given the authorities his soul, what he won't do is give them his good name. If he signs the confession and it's nailed to the church door where everyone can see it, then that reputation will be destroyed for good. In making this decision, John's thinking of his children and his children's children. If he signs that confession, then they'll have to live with the stigma and the shame for the rest of their lives. John knows that he's damned whatever he does. So at this crucial moment in his life he can only think about what's best for his family and their descendants.