Most scholars today don't believe that Peter authored 2 Peter, and there's also evidence that he didn't even write 1 Peter either. The author of these books obviously knew Greek very well; they knew the Greek Old Testament scriptures very well; they knew how to write in a compelling manner very well. However, based on the description we get from the Gospels of a fisher from the small town of Capernaum, it was highly unlikely that Peter would have known Greek or how to write.
In order to evaluate Peter's linguistic abilities, the place to begin, then, is with Capernaum. A full summary of what we know about Capernaum from Peter's day is provided by an American archaeologist of Palestine, Jonathan Reed. 2 On the basis of archaeological digs and historical sources, it is clear that Capernaum was a historically insignificant village in rural Galilee. It is never mentioned in any ancient source prior to the Gospels. It is scarcely mentioned by any sources after that...
The town is on none of the major international trade routes. The Roman roads in the area date from a hundred years after Peter's life. There is no trace of any pagan or Gentile population in the town. There are no inscriptions of any kind on any of the buildings. Reed concludes that the inhabitants were almost certainly 'predominantly illiterate.'
The town Peter came from almost certainly had no source of education or literacy, and in antiquity, there was no adult education for already grown adults seeking to become literate, let alone become well-skilled authors in a foreign language. Peter would've known Aramaic. Greek And beyond that, the author of Acts records that Peter was known to be an uneducated man.
But there is another major concern with 2 Peter. That is that the author of 2 Peter references the letters of Paul. These letters have been around and circulated long enough for people to start considering Paul's letters scripture (Something that Paul himself never does). So this has to have been written several years after Paul's death. However, Peter and Paul lived and died around the same time during the reign of Nero.
The gospels claim that Peter was an uneducated fisherman from a town where no one spoke Greek. How can Peter have written books at such a high level in a foreign language? Either Peter was an extremely well-educated man, or these books were not written by him.
2 Peter seems to be responding to the idea of people mocking Christians for saying "Jesus is coming soon". Peter refers to Paul's letters as "scripture", and talks about them after they have long circulated and been discussed. How is this all possible if Peter was writing at the same time as Paul was writing his own letters? These seem to be questions people would raise only after their deaths.