What are the aspects of the impossibility of God taking a son or having one?

There are many proofs for the impossibility of God having a son, among them:

1. Explicit Quranic texts that deny a son to God, such as His saying: ﴿Say: He is Allah, [the] One. Allah, the Eternal Refuge. He neither begets nor is born. Nor is there to Him any equivalent.﴾ and His saying: ﴿It is not for Allah to take a son; exalted is He.﴾ 2. The default state of things is non-existence. Whoever claims that God has a son is required to provide proof, and he will not find any. 3. A child resembles its parent, and there can be no equal to God. If we were to imagine a son for God, would he be originated or eternal? Both assumptions are untenable, because what is originated does not resemble what is eternal, and what is eternal cannot be a child. 4. The need for a child arises from the weakness of creatures and their need for support. Allah, glory be to Him, is free of all such needs; He is the Owner, the Disposer, and the Controller of the entire universe.