The problem of claiming that the Son is begotten with respect to his divine nature
Christian theology has it that the Second Person of the Trinity, the Divine Son, was incarnated in Jesus of Nazareth. The person of Jesus is the Second Person who necessarily possesses a divine nature and, given the historical event of the Incarnation, contingently possesses a human nature. This is the doctrine of the hypostatic union; Jesus is one person (i.e., one hypostasis) with two natures: one divine and one human. The divine and the human natures are united in the sense that both are possessed by the same person.
Arguably, aseity is a necessary condition for being divine. Whatever is divine exists a se. But to say that the Second Person was begotten from the First Person (the Father) is to say that the former is ontologically dependent on the latter and thus that the former lacks aseity. The Second Person can be begotten with respect to his human nature but not with respect to his divine nature since the divine cannot be ontologically dependent.
That’s the problem of claiming that the Son is begotten regarding his divine nature.
So far as I know, a Christian is not required to hold such a view, but it seems to me that some of the early fathers of the Church did affirm this position and, as such, were saddled with the associated problem. Perhaps some contemporary Christians hold this view as well.