Objection 1. It would seem that the procession of love in God is generation. For what proceeds by way of likeness of nature among living things is said to be generated and born. But what proceeds in God by way of love proceeds in the likeness of nature; otherwise it would be extraneous to the divine nature, and would be an external procession. Therefore what proceeds in God by way of love, proceeds as generated and born.
Objection 2. Further, as similitude is of the nature of the word, so does it belong to love. Hence it is said, that "every beast loves its like" (Sirach 13:19). Therefore if the Word is begotten and born by way of likeness, it seems becoming that love should proceed by way of generation.
Objection 3. Further, what is not in any species is not in the genus. So if there is a procession of love in God, there ought to be some special name besides this common name of procession. But no other name is applicable but generation. Therefore the procession of love in God is generation.
On the contrary, Were this true, it would follow that the Holy Ghost Who proceeds as love, would proceed as begotten; which is against the statement of Athanasius: "The Holy Ghost is from the Father and the Son, not made, nor begotten, but proceeding."
I answer that, The procession of love in God ought not to be called generation. In evidence whereof we must consider that the intellect and the will differ in this respect, that the intellect is made actual by the object understood residing according to its own likeness in the intellect; whereas the will is made actual, not by any similitude of the object willed within it, but by its having a certain inclination to the thing willed. Thus the procession of the intellect is by way of similitude, and is called generation, because every generator begets its own like; whereas the procession of the will is not by way of similitude, but rather by way of impulse and movement towards an object.
So what proceeds in God by way of love, does not proceed as begotten, or as son, but proceeds rather as spirit; which name expresses a certain vital movement and impulse, accordingly as anyone is described as moved or impelled by love to perform an action.
Reply to Objection 1. All that exists in God is one with the divine nature. Hence the proper notion of this or that procession, by which one procession is distinguished from another, cannot be on the part of this unity: but the proper notion of this or that procession must be taken from the order of one procession to another; which order is derived from the nature of the will and intellect. Hence, each procession in God takes its name from the proper notion of will and intellect; the name being imposed to signify what its nature really is; and so it is that the Person proceeding as love receives the divine nature, but is not said to be born.
Reply to Objection 2. Likeness belongs in a different way to the word and to love. It belongs to the word as being the likeness of the object understood, as the thing generated is the likeness of the generator; but it belongs to love, not as though love itself were a likeness, but because likeness is the principle of loving. Thus it does not follow that love is begotten, but that the one begotten is the principle of love.
Reply to Objection 3. We can name God only from creatures (13, 1). As in creatures generation is the only principle of communication of nature, procession in God has no proper or special name, except that of generation. Hence the procession which is not generation has remained without a special name; but it can be called spiration, as it is the procession of the Spirit.
Source: Summa Theologica (New Advent)