Diane said,
"The current title carries with it the risk of a human propensity: the "Us” vs "Them” worldview."
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Know ye not, that, the "Us” vs "Them” worldview is strewn throughout the Word of God!
"YOU are of God, little children, and have overcome THEM: because greater is he that is in YOU, than he that is in the WORLD. THEY are of the WORLD: therefore THEY speak from the WORLD, and the WORLD heareth THEM. WE are of God. He that knoweth God, heareth US; he that is not of God, heareth not US. By this we know the spirit of truth, and the spirit of error."
1 John 4:4-7
The above is just one clear sampling of this.
I make no apologies for "the current title" nor "the risk" you mention. For it is no human propensity to present it in such a way,it is the Divine Way in His Own Holy Word.
If I were to apologize, I would have to apologize for the Word of God. No christian would do such a thing.
As for the Hebrews passage you mentioned, you're absolutely right. It does just that, as you say,"explains how trials are a sign of God’s discipline = Fatherly love." The key word there is "Fatherly." We are not ignorant of the fact that God is not Father to all. As Jesus Himself told some, "your father is the devil." And in 1 John 3:10 it's stated,
"By this it is evident who are the children of God, and who are the children of the devil: whoever does not practice righteousness is not of God, nor is the one who does not love his brother."
"Us” vs "Them” worldview:
Children of light vs children of darkness
Children of God vs children of the devil
Sheep vs goats
Sons vs bastards
Saints vs sinners
Called out ones vs the world's ones
Vessels of mercy vs vessels of wrath
Those born of the Spirit vs those born of the flesh
Those whom He foreknew vs those He never knew
Any questions?
"My beloved is mine, and I am his; He pastures his flock among the lilies."
Song of Solomon 2:16