Peter says more than just that Jesus is the promised Messiah, the "Christ," but also that he is the Son of the Living God. This means that Peter understands Jesus to be more than just an especially glorious human being commissioned by God, but the Son of God himself. "He will be my son" reads God’s promise to David in 1 Chronicles 17:13. Likewise, we are not to regard Jesus’ words and ways as merely good advice from a great human teacher, but as coming from God himself.
However, this confession can only come from the inspiration of God: "Flesh and blood has not revealed this to you, but my Father who is in heaven." Even addressing Peter’s parentage speaks to this, as "Jonah" is also the Hebrew word for "dove." Peter then is truly a son of the Spirit to have made this confession.
So it is with all the baptized, that confessing and believing the divinity of Jesus Christ proves that we have spiritual parentage, and have been adopted into the life of the same heavenly Father who sent the Son.