2 Peter 2:1 But there were false prophets also among the people, even as there shall be false teachers among you, who privily shall bring in damnable heresies, even denying the Lord that bought them, and bring upon themselves swift destruction.

The only sign given here of a false teacher is heresy. Now we have to rely on the biblical understanding of heresy. Here are some of the listings found about heresy at BLB.ORG from an outline of bible usages.

Act of taking, capture: e.g. storming a city; a body of men following their own tenets (sect or party); dissensions arising from diversity of opinions and aims.

From Thayer’s Greek Lexicon let us add; that which is chosen, a chosen course of thought and action; hence one’s chosen opinion, tenet; according to the context, an opinion varying from the true exposition of the Christian faith

2 Timothy 4:3 For the time will come when they will not endure sound doctrine; but after their own lusts shall they heap to themselves teachers, having itching ears;

Titus 1:9 Holding fast the faithful word as he hath been taught, that he may be able by sound doctrine both to exhort and to convince the gainsayers.

How do you know that the teacher placed in a position of relating doctrine to your congregation is presenting sound doctrine? If you are in a sect created by a false prophet, this is all you have ever heard. This is all you will ever allow to be heard within that sect.

If you are in a church that has a history of being taught sound doctrine, then the obligation to examine that teacher before he or she is allowed to teach falls upon the elders. No teacher should be allowed to instruct the congregation without this examination.

The truth presented to a sect of the false prophet will be called heresy. The truth presented to true Christian faith will be received with a hardy Amen by the Holy Spirit in you.