Is faith a gift of God or a duty of man? It is both, as Hugh Martin explains in one of his sermons (see Christ for us):
Grace on his part, faith on your part: your faith in the sense that it comes from your believing heart, but his faith in that it is wrought by his Spirit there and prompted by his Word there.
I’m reminded by what a certain man once said to Jesus: “Lord, I believe; help thou my unbelief.” So, on the one hand, faith is a responsibility we ourselves exercise; on the other hand, we acknowledge that Jesus is the source and sustainer of our faith, i.e., the author and finisher of our faith.