This little fact was a way for Jesus to illustrate that the Gospel of Christ doesn't make an old nature new. What Christ gives when He comes into a person to save them is a brand new nature. Peter tells us we are partakers of a "divine nature" 2 Peter 1:4, and Paul tells us we become "new creations" 2 Corinthians 5:17 when we got saved. The old life we used to live can't be changed from its self-righteous religion. We never could save ourselves and even after salvation can our old nature live a new life. The new wineskins illustrate the new nature we have in Christ whereby the Holy Spirit lives the life of Christ in and through us. Our new nature is designed by God to live a new life.
We don't preach a gospel of reconstruction! We preach the Gospel of Resurrection, as Christ came back to life we are given His resurrected life to live! "Old things are passed away, all things become new!"