Passage
Peter saith to him: Why cannot I follow thee now? I will lay down my life for thee.
Peter saith to him: Why cannot I follow thee now? I will lay down my life for thee.
John 13:35 By this shall all men know that you are my disciples, if you have love one for another.
John 13:36 Simon Peter saith to him: Lord, whither goest thou? Jesus answered: Whither I go, thou canst not follow me now: but thou shalt follow hereafter.
John 13:37 Peter saith to him: Why cannot I follow thee now? I will lay down my life for thee.
John 13:38 Jesus answered him: Wilt thou lay down thy life for me? Amen, amen, I say to thee, the cock shall not crow, till thou deny me thrice.
The verse centers on "peter", "saith", "follow", "thee", "down", and "life". It is saying that the verse draws attention to "peter" and "saith", so its meaning should be read from those terms before moving to application.
The nearby context moves from verse 36's "Simon Peter saith to him Lord whither..." into verse 38's "Jesus answered him Wilt thou lay down...", so "peter" and "saith" belong inside that flow. In John context, the local focus is the identity of Jesus, new birth, eternal life, and belief and unbelief.
A plain takeaway is to answer the verse's own emphasis on "peter" and "saith" with trust shaped by these words, not by a vague optimism outside the passage.