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Except that Peter DID accept it from the Lord Himself:

I need your help. Where, in John 21:15-17 did Peter say anything except "...thou knowest that I love thee." ?

I do see Jesus rebuking Peter one more time, John 21:22, but no offer of "Popeship" to Peter nor acceptance by him.

¶ So when they had dined, Jesus saith to Simon Peter, Simon, [son] of Jonas, agapao thou me more than these? He saith unto him, Yea, Lord; thou knowest that I phileo thee. He saith unto him, Feed my lambs.
He saith to him again the second time, Simon, [son] of Jonas, agapao thou me? He saith unto him, Yea, Lord; thou knowest that I phileo thee. He saith unto him, Feed my sheep.
He saith unto him the third time, Simon, [son] of Jonas, phileo thou me? Peter was grieved because he said unto him the third time, phileo thou me? And he said unto him, Lord, thou knowest all things; thou knowest that I phileo thee. Jesus saith unto him, Feed my sheep.
John 21:15-17

The way I heard it explained:

Christ: Peter, do you love me more than these?
Peter: You know that I'm fond of you.
Christ: Feed my lambs.

Christ: Peter, do you love me?
Peter: You know that I'm fond of you.
Christ: Feed my sheep.

Christ: Peter, are you fond of me?
Peter: You know all things; you know that I'm fond of you.
Christ: Feed my sheep.

Thats way over simplified and sure to get flamed, but its something to think about.