Peter explains the purpose with the words “for a sincere brotherly love.” Sincere (unhypocritical) love is possible only as a result of appreciating “the truth” (the gospel of Jesus Christ). His work means Peter’s readers are now all children of God, which means they are brothers and sisters. So they want to act that way.
22 Having purified your souls by your obedience to the truth for a sincere brotherly love, love one another earnestly from a pure heart,