Why does the Son have a source of existence? Why does the Son have a source of existence?

Early church fathers believed that the Son has an source or origin of existence (reference).


To have an origin is different from having a beginning. Things could have an origin without having a beginning. For instance, the time a ball is placed onto a pillow, the cushion as well as the ball placed thereon are co-eval.


The source of the Son is the Father himself, the one who begat him from all eternity (cf. John 1:1; 1:18).The Father is expressedly identified as the fountain of the Godhead (source).

Note

This question is not about the Incarnation but about the eternal generation of the Son.
... his Son, with an origin,....

This is one of the classic misconception of Trinity. Jesus is not begotten in a particular point in time by The Father. As you have mentioned Jesus is eternally begotten. That is, in the very nature of God's existence, Jesus was/is/will-be begotten by the Father for eternity. This is same as how holy spirit was/is/will-be proceeding from the father (and the son). That is being eternally begotten is not an event in the past, rather the state of existence (being) of second person of the Trinity in the Trinity.