The selected passage of Scripture used by those who teach that Christ bore the sickness of mankind vicariously as He bore our sins is Matthew viii.17. But Christ at that moment was not making atonement. They vitiate the whole doctrine of atonement by making Christ live an atoning life. But Christ was not here making atonement, nor did He until some three years later. Neither did our Lord anywhere teach that sickness needed His death.
Sin is the only thing that demands expiation by blood.
He nowhere affirmed that there were any vicarious elements in His healing. He did believe, however, in the vicariousness of His death. If sickness needs atonement, then sickness implies a clouded conscience and broken fellowship with God as sin does. But such a cruel doctrine is denied by the most saintly men in the Church, who, in the direst sicknesses, have had sweetest fellowship with God. The most abiding spiritual lessons come from sickness.