The scholar will first go to Romans 3, and other scriptures, to realize all have sinned and live in a cursed state. God considers us unrighteous and has placed us under wrath due to our sin. Though we have been created in the image of God, we have no way of living with God. Further, there is absolutely nothing possible for us to think, say, or do that can change that fact. We are hopelessly lost to live out all our days basking in different levels and types of sin. Not only that, there is no legal way for us to absolve ourselves of sin. Our sin has convicted us and we stand guilty as charged before the Holy and Righteous Judge. This has to be the staring point to answer your question. It is a point we would do well to dwell upon from time to time but not with a goal of depression or hopelessness. We should have an attitude of praise because God has given us the way out.
In this condition, we could never be adopted and considered a child of God. Justice demands we be condemned. But of his own free will, Christ has freely offered His life for ours. Then too, it is of our own free will where we have freely accepted this offer. There has been no coercion or deception on behalf of either party so God is just when declaring us no longer guilty. “Now the act of condemning is not a matter of changing someone’s spiritual condition, of somehow infusing sin or evil. It is simply a matter of charging a person with wrong and establishing guilt. Correspondingly, the act of justifying is not a matter of infusing holiness into believers but of declaring them righteous” (Christian Theology - Millard J. Erickson). So our legal standing before God has been justly dealt with.
Now with the legal restrictions between us and God removed through justification, we can cry out, Abba, Father, because before that time we never had a spiritual father. John 1:12: “Yet to all who received him, to those who believe in his name, he gave the right to become children of God.” Paul notes that our adoption is a fulfillment of part of the plan of God: he predestined us to be adopted as his sons through Jesus Christ, in accordance with his pleasure and will (Eph 1:5). And in Galatians 4:4-5 Paul links adoption with justification: “But when the time had fully come, God sent his Son, born of a woman, born under the law, to redeem those under the law, that we might receive the full rights of sons.”
What are the benefits of this adoption? In light of the fact that God has forgiven us, Paul urges us to forgive others. We are to be kind and tenderhearted, since God our Father has not been grudging in forgiving us. In law one is not convicted or acquitted before the act in question takes place. Only after the act itself can the penalty be paid and the justification made. In stark contrast, we need not fear that God’s grace will cease and that we will be treated severely if we slip once.
Not only has God forgiven us, but we have been reconciled to him. God has shown his love for us by taking the initiative in restoring the fellowship damaged by our sin. There is also liberty for the children of God. The child of God is not a slave who obeys out of a sense of bondage or compulsion. We did not receive a spirit that makes us a slave again to fear, but we receive the Spirit of sonship. But do not use this freedom to indulge the sinful nature, rather, serve one another in love.
Adoption means that the Christian is the recipient of God’s fatherly care. Paul noted that “we are God’s children. Now if we are children, then we are heirs - heirs of God and co-heirs with Christ, if indeed we share in his suffering in order that we may also share in his glory” (Rom 8:16-17).
And finally, it should not be thought that God is indulgent or permissive. He is our heavenly Father, not our heavenly Grandfather. Thus, discipline is one of the features of our adoption. The letter to the Hebrews has a rather extended discussion of this subject (12:5-11). Quoting Proverbs 3:11-12, the writer comments: “Endure hardship as discipline; God is treating you as sons. For what son is not disciplined by his father?” Discipline may not be present at the moment of application, but it is beneficial in the long term. Love is concern and action for the ultimate welfare of another.
The child of God has been endowed with a great number of inalienable rights straight from the Almighty God of the universe. Further, we have been recipients while yet a sinner and in rebellion to such wonderful blessings. As such, what is it we are to be found doing? Living like God’s only non-adopted Son, Jesus Christ. Amen.
Being a child of God is wrapped up in all of the above. Our condemnation, our justification, our adoption, our benefits, and our praise. All of these have made possible our life with God.
If you can find it, the second edition of Christian Theology by Millard J. Erickson is filled with though provoking scholarly information and I have used parts of it in the above answer. Later editions are also good but the second edition has 1253 pages and the others have less.
Also, visit www.bible.org and simply search for “child of God”. There will be some good reading there.