No, a person who is born of a parent is not adopted. It is sad that there are many good translations of the Bible that use the word "adoption" instead of "sonship". Even my favourite NKJV Bible says, "For you did not receive the spirit of bondage again to fear, but you received the Spirit of adoption by whom we cry out 'Abba, Father'." (Romans 8:15)
We know in the context of this passage that it is talking about sonship, being born again with a new nature, once we believe in Jesus Christ. Hence, the Spirit Himself who indwells us bears witness with our spirit that we are children of God. (Romans 8:16) So, the word should have been "sonship" instead of "adoption". As you said, an adopted child does not have the life and DNA of the father; only a true child would. When we are born again, we have received His life in our spirit, as the Word also says, "But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ from the dead will also give life to your mortal bodies through His Spirit who dwells in you." (Romans 8:11)
Similarly, Paul wrote that we "are all sons (and daughters) of God through faith in Christ Jesus" in Galatians 3:26. He went on to write, "And because you are sons, God has sent forth the Spirit of His Son into your hearts, crying out, 'Abba, Father!' Therefore you are no longer a slave but a son, and if a son, then an heir of God through Christ." (Galatians 4:6-7)
My pastor also once shared that Jesus did not come to earth to make bad people good. He came to make dead people live. Because we were once all dead in our transgressions. (Ephesians 2:1) We were spiritually dead because of Adam's disobedience. (Romans 5:12) For God to save us from sin and death, He needed to give us a completely new life, not just give us an outward makeover or teach us good moral conduct by giving us laws and regulations to obey. A person may behave well outwardly, but the inner condition of his heart may remain unchanged.
King David knew he needed a life transformation, hence after he sinned, he prayed, "Create in me a clean heart, O God, and renew a steadfast spirit within me. Do not cast me away from Your presence, and do not take Your Holy Spirit from me." (Psalm 51:10-11) The prophet Jeremiah also wrote that "The heart is deceitful above all things, and desperately wicked; who can know it?" (Jeremiah 17:9) As if to top it all, the prophet Isaiah wrote, "The whole head is sick, and the whole heart faints. From the sole of the foot even to the head, there is no soundness in it, but wounds and bruises and putrefying sores; they have not been closed or bound up, or soothed with ointment." (Isaiah 1:5-6)
Isaiah was keenly aware of his sinful state in the presence of God when he said, "Woe is me, for I am undone! Because I am a man of unclean lips, and I dwell in the midst of a people of unclean lips; for my eyes have seen the King, the LORD of hosts." (Isaiah 6:5) He also wrote, "But we are all like an unclean thing, and all our righteousnesses are like filthy rags." (Isaiah 64:6) No matter how many good deeds we perform, as long as we are sinners without Christ, we fall short of the glory of God and are doomed to the lake of fire.
But thanks be to God, He has not left us without a Saviour, Jesus Christ. And the rest is history - HIS story. :) Haha!
The apostle Paul preached, "Be reconciled to God. For He made Him who knew no sin to be sin for us, that we might become the righteousness of God in Him." (2 Corinthians 5:20-21) At the cross, we see the love of God, for He sent His Son Jesus Christ to be the propitiation for our sins. At the cross, He took our sins and sicknesses, that we might take His righteousness and healing. It's a divine exchange.
Through Jesus' death, burial and resurrection, God has made us alive together with Christ, having forgiven us all trespasses. (Colossians 2:13) Hence, Paul wrote: "Therefore, if anyone is in Christ, he is a new creation; old things have passed away; behold, all things have been new. Now all things are of God..." (2 Corinthians 5:17-18) So, we know our old Adamic nature and all the curses that came with it have passed away, including death, sorrow, crying and pain. Instead, we have a new divine nature, and we are blessed with every spiritual blessing in Christ in the heavenly places. (Ephesians 1:3) We have a new spirit and a new heart, and God has put His Spirit within us and cause us to walk in His statutes. (Ezekiel 36:25-27)
Finally, Hebrews 12 confirms we are legitimate children of God, whom He chastens with His words (as an aside: not with sicknesses or accidents). "If you endure chastening, God deals with you as with sons; for what son is there whom a father does not chasten? But if you are without chastening, of which all have become partakers, then you are illegitimate and not sons." (Hebrews 12:7-8)
Thanks for the opportunity to study the Bible, afforded by your question. God bless you, sister Sandy. :)
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Brother Adziwa, yes, sister Sandy has a precious heart for the word of Christ, as a grace gift from our heavenly Abba Father. :)