Reflecting upon the dream-parable, I quickly realized that I was being taught that we can't take care of our own sins alone. We need Christ's hands and often the hands of His servants to catch us and help extract our "hooks".
Sometimes our "hooks" aren't sins. Uninvited trials negatively affect our souls when we respond with despair. As with sin, we need hands other than our own to help us when unfortunate events threaten to crush us. The Savior offers healing and refuge for all of God's children. He also employs his servants and angels to help carry His work of love forward.
Service is a vital force in our spiritually-thirsty world. Without it there would be no hope, healing, or true happiness. There would be no real purpose for our existence. Christ's ultimate act of service is the source of healing for all spiritual wounds. He's ready to run to our aid. We need only to have the faith to call for His saving hands when, as Peter, we begin to drown in our struggles.
3 Nephi 9:14