61 But God can never be anything but love, or anything but the Father: and He, Who loves, does not envy; He Who is Father, is wholly and entirely Father. This name admits of no compromise: no one can be partly father, and partly not. A father is father in respect of his whole personality; all that he is is present in the child, for paternity by piecemeal is impossible: not that paternity extends to self-generation, but that a father is altogether father in all his qualities, to the offsprings born of him.
According to the constitution of human bodies, which are made of dissimilar elements, and composed of various parts, the father must be father of the whole, since a perfect birth hands on to the child all the different elements and parts, which are in the father. The father is, therefore, father of all that is his; the birth proceeds from the whole of himself, and constitutes the whole of the child. God, however, has no body, but simple essence: no parts, but an all-embracing whole: nothing quickened, but everything living.
God is therefore all life, and all one, not compounded of parts, but perfect in His simplicity, and, as the Father, must be Father to His begotten in all that He Himself is, for the perfect birth of the Son makes Him perfect Father in all that He has. So, if He is proper Father to the Son, the Son must possess all the properties of the Father. Yet how can this be, if the Son has not the quality of prescience, if there is anything from His Author, which is wanting in His birth? To say that there is one of God's properties which He has not, is almost equivalent to saying that He has none of them. And what is proper to God, if not the knowledge of the future, a vision, which embraces the invisible and unborn world, and has within its scope that which is not yet, but is to be?
Source: On the Trinity (New Advent)