The issue of "regeneration" παλινγενεσίας (palingenesias), is not the issue in this passage; the fact that they are "unlearned and unstable" is not a determinant of the whether or not they have been "washed in the water of regeneration"(Tit. 3:5).
Rather, as 1 Pet. 2:3,
As newborn babes, desire the sincere milk of the word, that ye may
grow thereby:
3 If so be ye have tasted that the Lord is gracious.
We all start out as "new born babes", naturally. or spiritually. Those that "grow in the sincere milk of the word" mature, those that don't remain "unlearned and unstable", failing to heed proper warning and "
many shall follow their pernicious ways; by reason of whom the way of
truth shall be evil spoken of.(2 Pet. 2:2)
Here, Peter is speaking of false prophets who have subverted the flock. Nicolas, a deacon anointed in Acts 6:5, later became the leader of the Nicolaitans, a sect condemned by Jesus in Rev. 2:6, who "
were before of old ordained to this condemnation, ungodly men, turning
the grace of our God into lasciviousness, and denying the only Lord
God, and our Lord Jesus Christ."(Jude 1:4)
Paul's message of grace, or God's unmerited favor, can easily be interpreted as license by unlearned and unstable men; Paul himself states this in Rom. 6:15,
What then? shall we sin, because we are not under the law, but under
grace? God forbid!
and Peter merely reminds his readers to read the whole counsel of Paul's epistles, and not stumble on one particular point.
It is clear that Peter was "alive and well" and had read Paul's epistles, maybe not all of them, but all that he had written to date, therefore the argument that an anonymous writer wrote 2 Pet. is specious, unless further evidence can be presented that 2 Pet. was not written by the apostle.