***Of course it’s not really clear that Peter was ever installed as Pope.***
In the OT, the steward was the keeper of the keys.
Matt 16:
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8 When Jesus went into the region of Caesarea Philippi 9 he asked his disciples, “Who do people say that the Son of Man is?”
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They replied, “Some say John the Baptist, 10 others Elijah, still others Jeremiah or one of the prophets.”
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He said to them, “But who do you say that I am?”
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11 Simon Peter said in reply, “You are the Messiah, the Son of the living God.”
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Jesus said to him in reply, “Blessed are you, Simon son of Jonah. For flesh and blood 12 has not revealed this to you, but my heavenly Father.
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And so I say to you, you are Peter, and upon this rock I will build my church, 13 and the gates of the netherworld shall not prevail against it.
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I will give you the keys to the kingdom of heaven. 14 Whatever you bind on earth shall be bound in heaven; and whatever you loose on earth shall be loosed in heaven.”
Peter was the only one who answered correctly. He was made the steward of the Lord.