1 Peter 1:23
Being born again, not of corruptible seed, but of incorruptible,
by the word of God, which liveth and abideth for ever.
Man doth not live by bread only, but by every word that proceedeth out of the mouth of Jehovah doth man live (Deu. 8:3). Quoted in Mat. 4:4 and Luk. 4:4, being the Lord's first ministerial utterance in the days of His flesh. The words preface this, It standeth written. To live and to live continuously in the future, man must be begotten by the incorruptible seed, the Word, which will most surely result in the rebirth or resurrection from the dead.
We might understand it a bit better if we consider the begetting of our Lord, Who was begotten, not of blood, nor of the will of the flesh, nor of the will of man, but of God (John 1:13). And He was without sin. So the Spirit begetting of a man is a miraculous work and results in resurrection; all a new creation.
In John 3:1-2 Nicodemus comes by night to ask The Lord Jesus spiritual questions. Jesus Christ begins to answer in John 3:3. In John 3:5, the Lord makes it plain to Nicodemus that a man must be begotten of Spiritual Water, which is the Word of God (Eph 5:26) if he is to enter into The Kingdom of God. And in the next verse, John 3:6, he makes a comparison, showing that anything that is begotten of the flesh brings forth flesh (no evolution here), and that which is begotten of the Spirit brings forth a spiritual body in The Resurrection. In John 3:8, we are to understand that the pneuma, the Spirit (not wind), resides in those who are begotten, leading them where He wills and speaking through them as He wills. This is a great lesson for us yet today.
Note the usage of begotten in John 3:16 and John 3:18. He was God's Son because of a unique begetting.
In 1 Cor. 4:15, Paul reminds them that in Christ Jesus, he had begotten them through The Gospel. This is a slightly different angle on the usage of the word begotten, but it helps with the study of the word.
It is too bad that the translation of Gal. 4:23 has obscured the real truth. But he of the bondwoman was begotten 'after the flesh;' but he of the free woman (was begotten) 'by promise.' Think about this. In Gal. 4:24, the word 'gendereth' is still in the Greek, the word for beget. Also, in Gal. 4:29, we have the word born twice, but it is really beget or begotten. Notice the conclusion at the end of the verse. Professing Christians, but not begotten of the Spirit, are persecuting those who are begotten of the Spirit. 'Twas ever so.
Note another use of beget in 2 Tim. 2:23, But foolish and unlearned questions avoid, knowing that they do gender (beget) strifes. You may think of some similar passages in which this idea prevails.
1 Pet. 1:3 tells us a profound truth. "Blessed be the God and Father of our Lord Jesus Christ, Who hath begotten us again unto a living hope by the resurrection of Jesus Christ from the dead." This again echoes Deu. 8:3 and other passages mentioned. It is too bad that after using the word correctly, the translators changed it in 1 Pet. 1:23. There it should read, "Being begotten again, not of corruptible seed, but of incorruptible, by the Word of God, Which liveth and abideth forever."
So we are led to understand that this begetting is everlasting life; the alternative - perish.