Do you think Jesus had the authority to delegate His authority to Peter, as He did in in this verse?
No, Jesus is the rock .... Jesus has all authority ... not Peter.
Psalm 18:2
The Lord is my rock and my fortress and my deliverer, my God, my rock, in whom I take refuge, my shield, and the horn of my salvation, my stronghold.
1 Corinthians
And all drank the same spiritual drink. For they drank from the spiritual Rock that followed them, and the Rock was Christ.
1 Samuel 2:2
“There is none holy like the Lord; there is none besides you; there is no rock like our God.
Deuteronomy
“The Rock, his work is perfect, for all his ways are justice. A God of faithfulness and without iniquity, just and upright is he.
Isaiah 26:4
Trust in the Lord forever, for the Lord God is an everlasting rock.
Psalm 62:2
He only is my rock and my salvation, my fortress; I shall not be greatly shaken.
Psalm 89:26
He shall cry to me, ‘You are my Father, my God, and the Rock of my salvation.’
Matthew 7:24-25
“Everyone then who hears these words of mine and does them will be like a wise man who built his house on the rock. And the rain fell, and the floods came, and the winds blew and beat on that house, but it did not fall, because it had been founded on the rock.
Isaiah 17:10
For you have forgotten the God of your salvation and have not remembered the Rock of your refuge; therefore, though you plant pleasant plants and sow the vine-branch of a stranger,
2 Samuel 22:32
“For who is God, but the Lord? And who is a rock, except our God?
Psalm 19:14
Let the words of my mouth and the meditation of my heart be acceptable in your sight, O Lord, my rock and my redeemer.
Isaiah
Fear not, nor be afraid; have I not told you from of old and declared it? And you are my witnesses! Is there a God besides me? There is no Rock; I know not any.”
Luke 8:13
And the ones on the rock are those who, when they hear the word, receive it with joy. But these have no root; they believe for a while, and in time of testing fall away.
Psalm 94:22
But the Lord has become my stronghold, and my God the rock of my refuge.
Habakkuk 1:12
Are you not from everlasting, O Lord my God, my Holy One? We shall not die. O Lord, you have ordained them as a judgment, and you, O Rock, have established them for reproof.
Isaiah 51:1
“Listen to me, you who pursue righteousness, you who seek the Lord: look to the rock from which you were hewn, and to the quarry from which you were dug.
Jesus is the Head of the Church. The church is portrayed as a flock of sheep with Jesus as the chief shepherd. Jesus Himself said that there is only one shepherd; Him. We read Jesus saying the following:
And I have other sheep that are not of this fold. I must bring them also, and they will listen to my voice. So there will be one flock, one shepherd. (John 10:16 ESV)
Ephesians For the husband is the head of the wife even as Christ is the head of the church, his body, and is himself its Savior.
The Great Commission
(Mark 16:14–18)
16Meanwhile, the eleven disciples went to Galilee, to the mountain Jesus had designated. 17When they saw Him, they worshiped Him, but some doubted.
18Then Jesus came to them and said, “
All authority in heaven and on earth has been given to Me. 19Therefore go and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit, 20and teaching them to obey all that I have commanded you. And surely I am with you always, even to the end of the age.”
Philippine 2
9Therefore God exalted Him to the highest place
and gave Him the name above all names,
10that at the name of Jesus every knee should bow,
in heaven and on earth and under the earth,
11and every tongue confess that Jesus Christ is Lord,
to the glory of God the Father.
Jesus is exalted to the highest place ... not Peter