Commenting on John 6:51, Calvin says thusly:
As this secret power to bestow life, of which he has spoken, might be referred to his Divine essence, he now comes down to the second step, and shows that this life is placed in his flesh, that it may be drawn out of it. It is, undoubtedly, a wonderful purpose of God that he has exhibited life to us in that flesh, where formerly there was nothing but the cause of death. And thus he provides for our weakness, when he does not call us above the clouds to enjoy life, but displays it on earth, in the same manner as if he were exalting us to the secrets of his kingdom. And yet, while he corrects the pride of our mind, he tries the humility and obedience of our faith, when he enjoins those who would seek life to place reliance on his flesh, which is contemptible in its appearance.
But an objection is brought, that the flesh of Christ cannot give life, because it was liable to death, and because even now it is not immortal in itself; and next, that it does not at all belong to the nature of flesh to quicken souls. I reply, though this power comes from another source than from the flesh, still this is no reason why the designation may not accurately apply to it; for as the eternal Word of God is the fountain of life, (John 1:4,) so his flesh, as a channel, conveys to us that life which dwells intrinsically, as we say, in his Divinity. And in this sense it is called life-giving, because it conveys to us that life which it borrows for us from another quarter. This will not be difficult to understand, if we consider what is the cause of life, namely, righteousness. And though righteousness flows from God alone, still we shall not attain the full manifestation of it any where else than in the flesh of Christ; for in it was accomplished the redemption of man, in it a sacrifice was offered to atone for sins, and an obedience yielded to God, to reconcile him to us; it was also filled with the sanctification of the Spirit, and at length, having vanquished death, it was received into the heavenly glory. It follows, therefore that all the parts of life have been placed in it, that no man may have reason to complain that he is deprived of life, as if it were placed in concealment, or at a distance.