I should correct you here. It's not the same reasoning.
Cyril's reasoning is:
If A is the mother of B, and B is God, therefore A is the mother of God.
The reasoning you cite is:
If A is the mother of B and B is God, therefore A is God.
Quite different, and quite wrong in the orthodox view of the Incarnation, quite at odds with the fundamental creeds and teaching of the Church, and not at all the same reasoning.
....”It’s not the same reasoning”...
As the sounds of ‘Has God not Said’ echoes from the garden.