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I think Jesus was talking to Peter, you think he was talking to the group.

Nope; KNOW.

The text is plain:

Matthew 16:13-18
13. When Jesus came to the region of Caesarea Philippi, he asked his disciples, "Who do people say the Son of Man is?"
14. They replied, "Some say John the Baptist; others say Elijah; and still others, Jeremiah or one of the prophets."
15. "But what about you?" he asked. "Who do you say I am?"
16. Simon Peter answered, "You are the Christ, the Son of the living God."
17. Jesus replied, "Blessed are you, Simon son of Jonah, for this was not revealed to you by man, but by my Father in heaven.
18. And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it.
19. I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven."

Chapters and verses were invented later; as we all know...

When Jesus came to the region of Caesarea Philippi, he asked his disciples, "Who do people say the Son of Man is?" They replied, "Some say John the Baptist; others say Elijah; and still others, Jeremiah or one of the prophets." "But what about you?" he asked. "Who do you say I am?" Simon Peter answered, "You are the Christ, the Son of the living God." Jesus replied, "Blessed are you, Simon son of Jonah, for this was not revealed to you by man, but by my Father in heaven. And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it. I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven."

Reading the text we can see that Jesus is talking to the GROUP of disciples; and He is answered by the impulsive one - SIMON Peter.

After dealing with SIMON Peter, He states - to the group - "I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven."

Catholic teaching limits this to SIMON Peter.