Objection 1. It would seem that a divine person cannot be properly sent. For one who is sent is less than the sender. But one divine person is not less than another. Therefore one person is not sent by another.
Objection 2. Further, what is sent is separated from the sender; hence Jerome says, commenting on Ezekiel 16:53: "What is joined and tied in one body cannot be sent." But in the divine persons there is nothing that is separable, as Hilary says (De Trin. vii). Therefore one person is not sent by another.
Objection 3. Further, whoever is sent, departs from one place and comes anew into another. But this does not apply to a divine person, Who is everywhere. Therefore it is not suitable for a divine person to be sent.
On the contrary, It is said (John 8:16): "I am not alone, but I and the Father that sent Me."
I answer that, the notion of mission includes two things: the habitude of the one sent to the sender; and that of the one sent to the end whereto he is sent. Anyone being sent implies a certain kind of procession of the one sent from the sender: either according to command, as the master sends the servant; or according to counsel, as an adviser may be said to send the king to battle; or according to origin, as a tree sends forth its flowers. The habitude to the term to which he is sent is also shown, so that in some way he begins to be present there: either because in no way was he present before in the place whereto he is sent, or because he begins to be there in some way in which he was not there hitherto. Thus the mission of a divine person is a fitting thing, as meaning in one way the procession of origin from the sender, and as meaning a new way of existing in another; thus the Son is said to be sent by the Father into the world, inasmuch as He began to exist visibly in the world by taking our nature; whereas "He was" previously "in the world" (John 1:1).
Reply to Objection 1. Mission implies inferiority in the one sent, when it means procession from the sender as principle, by command or counsel; forasmuch as the one commanding is the greater, and the counsellor is the wiser. In God, however, it means only procession of origin, which is according to equality, as explained above (42, 4,6).
Reply to Objection 2. What is so sent as to begin to exist where previously it did not exist, is locally moved by being sent; hence it is necessarily separated locally from the sender. This, however, has no place in the mission of a divine person; for the divine person sent neither begins to exist where he did not previously exist, nor ceases to exist where He was. Hence such a mission takes place without a separation, having only distinction of origin.
Reply to Objection 3. This objection rests on the idea of mission according to local motion, which is not in God.
Source: Summa Theologica (New Advent)