Theopneustos [god-breathed] is a metaphor and therefore lacks any specificity. It is picturesque speech. What does it literally mean? No one knows though plenty claim they do.
I think the best we can say is that God is a spirit and as such he does not breath air. So this word is not referring to the breath of god. God does not have a breath except as we might speak anthropomorphically. So perhaps it is an anthropomorphic statement and if so then it is an analogy. Either way -- be it an analogy or a metaphor -- both linguistic functions are indirect linguistic constructs that do not make direct reference to a specific meaning. Both constructs function by leaving the clarity to the imagination of the hearer. That is how analogies and metaphors work.
Now speaking anthropomorphically, scripture is not the only thing god-breathed. The universe was "spoken" into existence, God said and it was so. The very nature of mankind is also god-breathed. Genesis 2:7 "the LORD God formed the man from the dust of the ground and breathed into his nostrils the breath of life, and the man became a living being."
So according to scripture there are three things that we can regard as God breathed, scripture, the universe, and human beings.
Do you want to know god-breathed truth? Then you had better accept the authority of biology, physics and the study of all things scientific. You should consider the various theories proposed to explain human behavior, be a student of sociology, psychology, philosophy , anthropology, political theory and economics. Then also include the phenomenon of scripture itself.
All three god-breathed items are self revealing and cannot be paid attention to without supplying one's own powers of observation, biases, conclusions and capacities. In other words, in spite of the supply of scientific data, human beings, and scripture you can never have any understanding of any of them without resorting to having your own personal opinion.
God can reveal these things to our perception but once revealed we can only perceive them and we alone make sense of them according to our capacity for making sense. Truth revealed is NOT synonymous with truth understood. That is the error and arrogance of fundamentalism. As useful and as authoritative and as credible as these god-breathed things are, there is still no room for a fundamentalist certainty about any of it.
We walk by faith. Not faith in a teaching or a fundamental assertion, but faith in the person of God whether understood or misunderstood we place our faith in HIM. We place our faith in the cross, not in the doctrine of the atonement, but in the event itself. It is what it is understood or misunderstood. I do not place my faith in the event of the cross as I understand it I simply place my faith in the event itself and let God worry about its "proper" understanding.
Christianity is not and never was a Gnostic reality of academic asserted truths. Christianity has always been the authenticity of the person of Jesus himself and the events of his life as they happened historically. And this is without regard to how one does or does not accurately make sense of it.