Thomas Aquinas, Compendium of Theology

Although the Son of God is said to have been made flesh and to have been conceived by the Holy Spirit and of the Virgin Mary, we are not to conclude that the Holy Spirit is the father of the man Christ, even though the Blessed Virgin is called His mother.

The first reason for this is that everything pertaining to the idea of mother is verified in the Blessed Virgin Mary. She furnished the matter to be formed by the Holy Spirit for the conception of Christ, as the idea of motherhood requires. But not all the elements required for the idea of fatherhood are found on the part of the Holy Spirit. The idea of fatherhood requires that the father produce from his nature a son who is of like nature with himself. Therefore if some agent would make a thing that is not derived from its own substance, and would not produce such a thing unto the likeness of its own nature, that agent could not be called the thing's father. We do not say that a man is the father of things he makes by plying an art, unless perhaps in a metaphorical sense. The Holy Spirit is, indeed, connatural with Christ as regards the divine nature; in this respect, however, He is not the father of Christ, but rather proceeds from Him. With respect to the human nature, the Holy Spirit is not connatural with Christ. For the human nature in Christ is other than the divine nature, as we said above. Nor is anything of the divine nature changed into human nature, as we also said above. Consequently the Holy Spirit cannot be called the father of the man Christ.

Moreover, that which is of greater moment in any son comes from his father, and what is secondary comes from his mother. Thus in other animals the soul is from the father, and the body from the mother. In man, of course, the rational soul does not come from the father, but is created by God; yet the power of the paternal seed operates dispositively toward the form. But that which is the greater in Christ, is the person of the Word, who is in no way derived from the Holy Spirit. We conclude, therefore, that the Holy Spirit cannot be called the father of Christ.