“And beside this, giving all diligence, add to… brotherly kindness, charity;” 2 Peter 1:5-7

The word of God says love the brethren, be kind! Then he says add to brotherly kindness, love- agape. The love that considers others in victory before itself!
“She (love) bears up under everything; believes the best in all; there is no limit to her hope, and never will she fall.”  1 Corinthians 13:7
“…love covers a multitude of sins.”  1 Peter 4:8
He wants you to express such characteristics towards others; endure all things with anticipation, hope for the best, and learn to look beyond the short coming of others.
Jesus is our prime example, he had told his disciples:
“Whosoever therefore shall be ashamed of me and of my words in this adulterous and sinful generation; of him also shall the Son of man be ashamed, when he cometh in the glory of his Father with the holy angels.”  Mark 8:38
But Peter obviously didn’t get the message:
“And the second time the cock crew. And Peter called to mind the word that Jesus said unto him, Before the cock crow twice, thou shalt deny me thrice. And when he thought thereon, he wept.”  Mark 14:72
Based on what Jesus had said, it would only mean Peter was doomed for life, and amongst the angels, Peter would be persona non grata, but after his resurrection:
“And entering into the sepulchre, they saw a young man sitting on the right side, clothed in a long white garment; and they were affrighted. And he saith unto them… tell his disciples and PETER that he goeth before you into Galilee:…” Mark 16:5,7
The angel did mention Peter’s name, not for evil but for good; Jesus’ love covered his shortcoming, because above all it was definite that Peter loved Jesus, that was why he followed him to Caiaphas’ house in the first place.
“And walk in love, as Christ also hath loved us”  Ephesians 5:2