We see in Paul's sending Timothy his Son to his rebellious children a reflection of God who sent His Son, Jesus Christ, to His rebellious children. All those who listen to Him and repent will not have to fear God's punishment, because they will be found faithful in Christ when the Father comes. Likewise all the Corinthians who listened to Timothy and repented would not have to fear father Paul when came, because they would be found faithful in Timothy. Honor your heavenly Father now by believing in the Son whom He sent ahead of Him to teach you His own words, so that He will honor you and bless you when He comes. Paul wraps up his metaphor of himself as the Corinthians' father with a rhetorical question.
Embraces are for the faithful child.
But perhaps the most glorious lesson to be learned in this text is something accidental. For here we get a glimpse of what it looks like to be united to Christ and to represent Christ as an ambassador in His kingdom. Paul's dealings with the Corinthians are strikingly correspond with God's redemptive-historical dealings with His children. His sending of Timothy is superimposed with the imagery of God's sending of Christ. His future coming is cast in the language of Christ's parousia.