As the author does not refer to himself as 'John' but as the presbyter, or 'elder' (2 John 1:1; 3 John 1:1), I will use that term to refer to him. The attribution to John only came later in the second century. I will look at the epistle as a whole and establish the context before returning to how and why the elder speaks of being born of God.
The elder's community is facing an existential crisis and he must use all his skills to save it. W. Hall Harris III ('3. The Author’s Opponents and Their Teaching in 1 John') says 1 John 2:19 provides good reason for thinking that a split has taken place in the Johannine community and the author’s opponents now constitute a community of their own, thoroughly committed to spreading their understanding of who Jesus is. The former members are approaching those who remain behind and seeking to convert them:
1 John 2:26 (KJV): These things have I written unto you concerning them that seduce (πλανώντων - 'lead astray') you.
It is this threat that the elder is dealing with. Burton L. Mack says, in Who Wrote the New Testament, pages 215-218, that the author of First John accuses his erstwhile brothers and sisters of hating those who remain with the community, and therefore both of being liars and of not loving God, even referring to them as the antiChrist or of being in league with the devil. In contrast, the members of the elder's flock are sinless as long as they remain loyal to him, part of the true faith.
1 John 3:8-9 uses hyperbole to contrast the former members of the community, sinners in league with the devil, with the elder's followers, who can not continue sinning (ἁμαρτάνειν):
1 John 3:8: He that committeth sin is of the devil; for the devil sinneth from the beginning. For this purpose the Son of God was manifested, that he might destroy the works of the devil.
1 John 3:9: Whosoever is born of God doth not commit sin; for his seed remaineth in him: and he cannot sin, because he is born of God.
The others may have said Jesus was not the Christ (as the elder implies in l John 2:22) or that the real (divine) Jesus did not “come in the flesh” at all (1 John 4:2-3), but those are accusations that the makes good use of in chapter 5, saying in 5:1:
1 John 5:1: Whosoever believeth that Jesus is the Christ is born of God: and every one that loveth him that begat loveth him also that is begotten of him.
Having told the faithful that by believing Jesus is the Christ they are born of God, he goes on to say that by this faith they overcome the world:
1 John 5:4: For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith.
The elder is not addressing the issues of the wider church, so what he says should not be read too readily as applying to Christians in general and to our time. We can read from his hyperbole that he believed that people can be born of God after natural birth, but in any case this was only intended as a symbolic statement, given to encourage members of the community to remain true to their faith and not follow the 'perverted' teachings of those who had left the community.