Perhaps you misunderstand Paul's intent, because Paul quotes from a couple of the Greek poets of their day. These quotes were designed to qualify the truth in what he was saying in order to make it more palatable to them.
Paul was teaching them that people are God's offspring in the sense they have all been created in His image as creator. That's quite different than "Every one who believes that Jesus is the Christ is a child of God, and every one who loves the parent loves the child."
Do you recognize the difference?
The best way to put things into context is to express the idea the way modern writers would express it.
For example, when the original writer says someone is a son of the devil, what he means is that the person is the product of his decision to let his worldly nature have primacy in his life.
Why did the ancients personalise the worldly nature, call it the devil? To assign responsibility, maybe even acknowledge good acts, and reward it, with recognition of it, or justification, or bad, and pass judgment.
That's why Paul says that while he serves God with his (redeemed) mind, which is seated with Christ in high places, he finds a different force in action, in his yet to be redeemed body. It is not he who sins, but Mr Sin. He is talking about his worldly nature.
The writers of Scripture did not only personalise the worldly nature, the blind and thoughtless drive, seen in its vicious overrunning of competitors, for life preserving resources, but also the thoughtful one. Wisdom is seen as a woman, whose work, children, will be prove her to be right. That's two instances of personalisation right there, a very common Jewish literary device.
But why did the writers call the worldly nature as Sin? Other creatures in nature also have this selfish gene, competing with other species, and sometimes with their own species. Baby sharks eat their siblings in the womb, yet no one calls them sinners. A tiger escapes from a zoo and kills a passerby, but isn't put on trial and punished. How is it their acts are not crimes or sin, and human acts of striving for survival are? It is because of the principle of culpability. Men know good from evil. They are competent.
So when a text says:
1 John 3
8The one who practices sin is of the devil, because the devil has been sinning from the very start. This is why the Son of God was revealed, to destroy the works of the devil.
The modern writer will put it this way:
The one who practices sin is allowing himself to be a product of his worldly nature, because the worldly nature has been sinning from the very start. This is why the Son of God was revealed,
to destroy the works of the worldly nature.
Don't forget, this selfish gene is the engine for the survival of all forms of life. If there were no drives, no pleasure derived from satisfying hunger, how will any species grow and reproduce? But it does almost acquire a life of its own, even using reason and logic, to lie that it's the only option. Read how it interacts with Eve and with Christ. We are ourselves familiar with the arguments we have with it in our daily lives. Who needs the devil, when we have a personal live in scrounge, who is always advocating the easy, broader path. However, it forgets about the involvement of God in the decision to be selfless.
Luke 7
35"Yet wisdom is vindicated by all her children."
Isaiah 11
8The infant will play by the cobra's den, and the toddler will reach into the viper's nest.
Isaiah 65
25The wolf and the lamb will feed together, and the lion will eat straw like the ox, but the food of the serpent will be dust. They will do no harm nor destruction on all My holy mountain," says the LORD.
As for the difference between the universality of all men being created in God's image and some men being special by virtue of loving Christ, I think Paul is simply saying that his listeners also were part of the unconditional concern God had, being his children, supported by their own wise men. He never denies that truth, it would be counterproductive to support non Scriptural ideas, and that truth is seen in the teaching that all men are created in that image, supports the idea strongly that all men are indeed sons of God, like Adam.