Why is he called God’s only begotten Son, since we also are children of God?

Because Christ alone is the eternal, natural Son of God; but we are children of God by adoption, through grace, for Christ’s sake.

Article 7: Election is the unchangeable purpose of God, whereby, before the foundation of the world, he hath out of mere grace, according to the sovereign good pleasure of his own will, chosen, from the whole human race, which had fallen through their own fault, from their primitive state of rectitude, into sin and destruction, a certain number of persons to redemption in Christ, whom he from eternity appointed the Mediator and Head of the elect, and the foundation of Salvation.

This elect number, though by nature neither better nor more deserving than the others, but with them involved in one common misery, God hath decreed to give to Christ, to be saved by him, and effectually to call and draw them to his communion by his Word and Spirit, to bestow upon them true faith, justification and sanctification; and having powerfully preserved them in the fellowship of his Son, finally, to glorify them for the demonstration of his mercy, and for the praise of his glorious grace; as it is written: “According as he hath chosen us in him, before the foundation of the world, that we should be holy, and without blame before him in love; having predestinated us unto the adoption of children by Jesus Christ to himself, according to the good pleasure of his will, to the praise of the glory of his grace, wherein he hath made us accepted in the beloved,” Ephesians 1:4,5,6.And elsewhere: “Whom he did predestinate, them he also called; and whom he called, them he also justified; and whom he justified, them he also glorified,” Romans 8:30.

Article 10: The good pleasure of God is the sole cause of this gracious election; which doth not consist herein, that out of all possible qualities and actions of men God has chosen some as a condition of salvation; but that he was pleased out of the common mass of sinners to adopt some certain persons as a peculiar people to himself, as it is written, “For the children being not yet born neither having done any good or evil,” etc., it was said (namely to Rebecca): “the elder shall serve the younger; as it is written, Jacob have I loved, but Esau have I hated,” Romans 9:11,12,13.”And as many as were ordained to eternal life believed,” Acts 13:48.

Article 6: But God, who is rich in mercy, according to his unchangeable purpose of election, does not wholly withdraw the Holy Spirit from his own people, even in their melancholy falls; nor suffers them to proceed so far as to lose the grace of adoption, and forfeit the state of justification, or to commit sins unto death; nor does he permit them to be totally deserted, and to plunge themselves into everlasting destruction.