A few brief thoughts on this.
1. Note how Peter introduces himself in his two epistles. In the first, it's "Peter, and apostle of Jesus Christ" (1 Pt. 1:1); in the second, it's "Simon Peter, a servant and an apostle of Jesus Christ" (2 Pt. 1:1). Peter was the name given to him by Christ to signify his spiritual strength, Simon his birth name, pointing to his humanity and weakness. Perhaps he is intimating by adding "Simon" that, "I may be an apostle, but I'm merely a man" (Acts 10:26). Also note how in 2 Pt. 1:1 "servant" precedes "apostle." Seems quite a bit humbler, doesn't it, to add servant and mention it before his apostleship? Compare Paul's self-introduction in Rom. 1:1, "Paul, a servant of Jesus Christ, called to be an apostle..."
2. Notice that Peter's epistles emphasize spiritual growth, from start to finish. He mentions it in 1 Pt. 2:2, 1 Pt. 5:10 ("make you perfect"), 2 Pt. 1:5-8, and 2 Pt. 3:18 (his last recorded words!). To be burdened about others' spiritual growth is evidence of one's own.
3. When Peter and John are arraigned before the council of Jewish elders in Acts 4, they are classified as "unlearned and ignorant men" (Acts 4:13). But, wow, how the tables are turned at the end of Peter's life! Please read 2 Peter 3:5, 8, and 16. In these passage, Peter speaks of others' ignorance (vv. 5, 8) and of them being unlearned (v. 16). He may have seemed ignorant and unlearned to the Jewish elders, but in reality they, and those mentioned in 2 Pt. 3 turn out to be the ignorant and unlearned ones. In 2 Pt. 3:16, Peter also rebukes certain men's instability, and prays for God to "stablish" kingdom saints (1 Pt. 5:10), signifying his own stability, in contrast to his instability before Pentecost.
Truly, the apostle Peter demonstrates remarkable spiritual growth for us and lived what he taught!