What this author is trying to convey is who are the false prophets/teachers and gives them a warning about the coming Judgement Day. It is mainly people who are in denial of Judgement Day and question whether or not it will come. According to the book of 2 Peter, many of the false prophets are among the people so it is very hard to tell who is a false prophet. However, a good way to tell one is their beliefs. If they deny that they were brought into Earth by God and bring in destructive opinions (something that is considered sinful), then that person is a false prophet. The author characterized the false prophets as the people who were in denial in the story of Noah, citizens of Sodom and Gomorrah and enemies of Lot. The author wants people to know that God will punish those people when he comes for Judgement.
When the author was talking about the Greco-Roman people, he is basically saying that the Greco-Romans are also people in denial. He wants them to know that the religion of Christianity is a legitimate one. The catastrophic events that has happened before were basically a life lesson. They should know the teachings of the Lord in order to be saved when God comes for Judgement. He doesn’t want them to be lured by false people or have them spread their false teaching. They don’t know what is coming to them.
If I was a second-century Christian reading this letter, I, myself, would try to spread the religion. The second letter of Peter and the Gospel of Matthew is enough to conceive me that Jesus is the true son of God. Peter saw it for himself. So, he know that we all must follow to word of the Lord. That is what God and Jesus wanted us to do, so I will legitimize the religion and spread it.