The incarnate Son remains the Father's own Son by nature
Cyril is commenting on Psalm 2:7, where the Father addresses Christ, and is explaining how the eternal Son became flesh without ceasing to be the Father's own Son.
The one who alone knows the Father and is known by the Father alone, his wisdom and word, the angel of great counsel, makes the mystery of the plan of salvation with flesh very clear to us. For though he is Son by nature and truly, and though he has shone forth from the very essence of God the Father, he became flesh—that is, a human being—and underwent birth according to the flesh among us, even though he is eternal and always co-existing with the one who begot him. Yet even though he became flesh, the Father knows him as his own Son even in this state. For he said, "The Lord said to me: 'You are my Son; today I have begotten you'" (Psalm 2:7).
Greek
Κύριος εἶπεν πρός με Υἱός μου εἶ σύ, ἐγὼ σήμερον γεγέννηκά σε. Ὁ μόνος εἰδὼς τὸν Πατέρα καὶ ὑπὸ μόνου γινωσκόμενος τοῦ Πατρός, ἡ σοφία καὶ ὁ λόγος αὐτοῦ, ὁ τῆς μεγάλης βουλῆς ἄγγελος, τῆς μετὰ σαρκὸς οἰκονομίας ἡμῖν τὸ μυστήριον εὖ μάλα διατρανοῖ. υἱὸς γὰρ ὢν φύσει καὶ ἀληθῶς, καὶ ἐξ αὐτῆς ἀναλάμψας τῆς οὐσίας τοῦ Θεοῦ καὶ Πατρός, γέγονε σάρξ, τουτέστιν ἄνθρωπος, καὶ τὴν κατὰ σάρκα μεθ' ἡμῶν ὑπέστη γέννησιν, καίτοι προαιώνιος ὢν καὶ ἀεὶ συνυφεστηκὼς τῷ γεγεννηκότι. πλὴν εἰ καὶ γέγονε σάρξ, ἴδιον ὄντα υἱὸν οἶδεν αὐτὸν καὶ οὕτως ὁ Πατήρ, ἔφη γάρ Κύριος εἶπε πρός με· Υἱός μου εἶ σύ, ἐγὼ σήμερον γεγέννηκά σε.