The antichrists were claiming faith in God while denying and opposing the Son. To do, John says, is impossible. Because Jesus is God's Son and the Messiah, anyone who denies the Son doesn't have the Father either. And, anyone who confesses the Son also has the Father. Many cultists today call themselves Christians, but they deny the deity of Jesus Christ.
True believers, who had been begotten of God had received the Holy Spirit to help the discern truth and reject falsehood. They didn't need another teacher. Persevering in the relationship with Christ ensures that believers will remain faithful.