False teachers, just like false prophets, have an ungodly (nefarious) purpose. Specifically they are responsible for introducing heresies. At the time of writing, heresy was a term used to refer to sects (see Acts 5:17; Acts 15:5; Acts 26:5) or a particular faction in church (Galatians 5:20; 1 Corinthians 11:18).1 From this, the term developed to be understood as a reference to false doctrine, specifically teaching that deviates from apostolic orthodoxy. The introduction of heresies then is the introduction of new teaching that contradicts the truth which has been shared by apostles like Peter. This teaching is destructive since it leads away from Christ to hell.2
In the case of 2 Peter 1–3, the heretics in question denied the coming of the Lord and future judgment (2 Peter 3:4). This perspective was joined with a carefree morality (2 Peter 2:14, 2 Peter 2:18–19; 2 Peter 3:3–9) as well as a disregard for the apostolic and prophetic heritage (2 Peter 1:16–21).3
1 But false prophets also arose among the people, just as there will be false teachers among you, who will secretly bring in destructive heresies, even denying the Master who bought them, bringing upon themselves swift destruction.