This is tricky. So someone correct me if I’m off here. Men have spiritual souls. The body and the spiritual soul are one nature, not a duality… the soul being spiritual is not a duality… our body, soul and spirit are really one nature. Angels and God are pure spirit, non-corporeal.
328 The existence of the spiritual, non-corporeal beings that Sacred Scripture usually calls “angels” is a truth of faith. The witness of Scripture is as clear as the unanimity of Tradition.
330 As purely *spiritual *creatures angels have intelligence and will: they are personal and immortal creatures, surpassing in perfection all visible creatures, as the splendor of their glory bears witness.190
362 The human person, created in the image of God, is a being at once corporeal and spiritual. The biblical account expresses this reality in symbolic language when it affirms that "then the LORD God formed man of dust from the ground, and breathed into his nostrils the breath of life; and man became a living being."229 Man, whole and entire, is therefore *willed *by God.
365 The unity of soul and body is so profound that one has to consider the soul to be the “form” of the body:234 i.e., it is because of its spiritual soul that the body made of matter becomes a living, human body; spirit and matter, in man, are not two natures united, but rather their union forms a single nature.
CCC 367 Sometimes the soul is distinguished from the spirit: St. Paul for instance prays that God may sanctify his people “wholly”, with “spirit and soul and body” kept sound and blameless at the Lord’s coming.236 The Church teaches that this distinction does not introduce a duality into the soul.237 “Spirit” signifies that from creation man is ordered to a supernatural end and that his soul can gratuitously be raised beyond all it deserves to communion with God.238
I guess our spiritual soul is sort of a bridge that unites the material of the body with the spiritual in one nature and makes us destined for eternal life, not just a material soul like an animal destined to have both body and soul die and not eternal and not spiritual beings.