Objection 1. It would seem that Christ is not the Head of men as to their bodies. For Christ is said to be the Head of the Church inasmuch as He bestows spiritual sense and the movement of grace on the Church. But a body is not capable of this spiritual sense and movement. Therefore Christ is not the Head of men as regards their bodies.
Objection 2. Further, we share bodies with the brutes. If therefore Christ was the Head of men as to their bodies, it would follow that He was the Head of brute animals; and this is not fitting.
Objection 3. Further, Christ took His body from other men, as is clear from Matthew 1 and Luke 3. But the head is the first of the members, as was said above (1, ad 3). Therefore Christ is not the Head of the Church as regards bodies.
On the contrary, It is written (Philippians 3:21): "Who will reform the body of our lowness, made like to the body of His glory."
I answer that, The human body has a natural relation to the rational soul, which is its proper form and motor. Inasmuch as the soul is its form, it receives from the soul life and the other properties which belong specifically to man; but inasmuch as the soul is its motor, the body serves the soul instrumentally. Therefore we must hold that the manhood of Christ had the power of "influence," inasmuch as it is united to the Word of God, to Whom His body is united through the soul, as stated above (Question 6, Article 1). Hence the whole manhood of Christ, i.e. according to soul and body, influences all, both in soul and body; but principally the soul, and secondarily the body: First, inasmuch as the "members of the body are presented as instruments of justice" in the soul that lives through Christ, as the Apostle says (Romans 6:13): secondly, inasmuch as the life of glory flows from the soul on to the body, according to Romans 8:11: "He that raised up Jesus from the dead shall quicken also your mortal bodies, because of His Spirit that dwelleth in you."
Reply to Objection 1. The spiritual sense of grace does not reach to the body first and principally, but secondarily and instrumentally, as was said above.
Reply to Objection 2. The body of an animal has no relation to a rational soul, as the human body has. Hence there is no parity.
Reply to Objection 3. Although Christ drew the matter of His body from other men, yet all draw from Him the immortal life of their body, according to 1 Corinthians 15:22: "And as in Adam all die, so also in Christ all shall be made alive."
Source: Summa Theologica (New Advent)