Objection 1. It would seem that the soul was not made, but was God's substance. For it is written (Genesis 2:7): "God formed man of the slime of the earth, and breathed into his face the breath of life, and man was made a living soul." But he who breathes sends forth something of himself. Therefore the soul, whereby man lives, is of the Divine substance.
Objection 2. Further, as above explained (75, 5), the soul is a simple form. But a form is an act. Therefore the soul is a pure act; which applies to God alone. Therefore the soul is of God's substance.
Objection 3. Further, things that exist and do differ are the same. But God and the mind exist, and in no way differ, for they could only be differentiated by certain differences, and thus would be composite. Therefore God and the human mind are the same.
On the contrary, Augustine (De Orig. Animae iii, 15) mentions certain opinions which he calls "exceedingly and evidently perverse, and contrary to the Catholic Faith," among which the first is the opinion that "God made the soul not out of nothing, but from Himself."
I answer that, To say that the soul is of the Divine substance involves a manifest improbability. For, as is clear from what has been said (77, 2; 79, 2; 84, 6), the human soul is sometimes in a state of potentiality to the act of intelligence -- acquires its knowledge somehow from things--and thus has various powers; all of which are incompatible with the Divine Nature, Which is a pure act--receives nothing from any other--and admits of no variety in itself, as we have proved (3, 1,7; 9, 1).
This error seems to have originated from two statements of the ancients. For those who first began to observe the nature of things, being unable to rise above their imagination, supposed that nothing but bodies existed. Therefore they said that God was a body, which they considered to be the principle of other bodies. And since they held that the soul was of the same nature as that body which they regarded as the first principle, as is stated De Anima i, 2, it followed that the soul was of the nature of God Himself. According to this supposition, also, the Manichaeans, thinking that God was corporeal light, held that the soul was part of that light bound up with the body.
Then a further step in advance was made, and some surmised the existence of something incorporeal, not apart from the body, but the form of a body; so that Varro said, "God is a soul governing the world by movement and reason," as Augustine relates (De Civ. Dei vii, 6 [The words as quoted are to be found iv. 31.) So some supposed man's soul to be part of that one soul, as man is a part of the whole world; for they were unable to go so far as to understand the different degrees of spiritual substance, except according to the distinction of bodies.
But, all these theories are impossible, as proved above (3, 1,8 and 75, 1), wherefore it is evidently false that the soul is of the substance of God.
Reply to Objection 1. The term "breathe" is not to be taken in the material sense; but as regards the act of God, to breathe [spirare], is the same as to "make a spirit." Moreover, in the material sense, man by breathing does not send forth anything of his own substance, but an extraneous thing.
Reply to Objection 2. Although the soul is a simple form in its essence, yet it is not its own existence, but is a being by participation, as above explained (75, 5, ad 4). Therefore it is not a pure act like God.
Reply to Objection 3. That which differs, properly speaking, differs in something; wherefore we seek for difference where we find also resemblance. For this reason things which differ must in some way be compound; since they differ in something, and in something resemble each other. In this sense, although all that differ are diverse, yet all things that are diverse do not differ. For simple things are diverse; yet do not differ from one another by differences which enter into their composition. For instance, a man and a horse differ by the difference of rational and irrational; but we cannot say that these again differ by some further difference.
Source: Summa Theologica (New Advent)