You might be thinking it is easy to answer this question.

But this was a big question for the disciples to answer then, because they are seeing Jesus physically in the image of man.

Come to think of it, they can actually replied, you are the Boss, Teacher, Master, Rabbi, Mentor and so on.

But Peter replied you are Christ, the son of the living God. (Matthew 16:16)

Oh What a wonderful response Jesus sensed in the spirit that God himself revealed unto Peter. (Matthew 16:17)

But why is it Peter that could answer the question? 🤔

Peter knew from the beginning that Jesus is not an ordinary man.

When Jesus met Peter from the beginning catching fish with net, He said follow me, and I will make you fishers of men. 
Peter was so inquisitive to know how to be catching men with net, it looks funny right? Maybe not.
Then He knows Jesus is a wonder man. So He followed Jesus to learn that new skills of fishers of men not fishers of fish.

What to learn here is the preparedness of Peter to learn from Jesus and also to know the Wonders Jesus carries.

Bringing the discussion to our initial question, why Peter could answer the question through revelation.
God saw Peter preparedness to know who Jesus is, that's why He revealed to him that Peter, Jesus Christ is my son.

And Peter responded to Jesus, You are Christ the Son of the living God.

Key Note:
Your preparedness matters alot in anything that you do.

Therefore are you prepared for the Kingdom of God?

Only people that are prepared, God will give the grace to see His Kingdom.