And since many saints participate in the Holy Spirit, He cannot therefore be understood to be a body, which being divided into corporeal parts, is partaken of by each one of the saints; but He is manifestly a sanctifying power, in which all are said to have a share who have deserved to be sanctified by His grace. (Book I, Section 3)

Origen is, I perceive, working his way through a very Greek problem: How to distinquish between the physical and spiritual or body and mind or flesh and soul.

This dualistic frame of reference can be found in Plato's Phaedo and in much of Western thinking ever since. It is a recurring feature in Paul's epistles.

I do not perceive the issue was important to Jesus. Where the Greeks sought clarity in distinction, Jesus preferred a Jewish embrace of wholeness.