“The Lord is risen indeed, and has appeared to Simon” (Luke 24:34) The second appearance of the resurrected Jesus was to Peter. It was a private, personal meeting, and all we know about it is what this verse tells us. We don’t know what was said or what transpired. It was for Peter and Jesus only.
Most likely, it was because Peter had denied Jesus. He had bragged he would die for Jesus, but Jesus told him instead of dying, he would be denying Him three times. When Peter did utter that third denial, Jesus “turned, and looked upon Peter.” (Lk 22:61). This wasn’t a “I told you so” look, but one of compassion. But Peter ran off and wept bitterly over his failure to Jesus.
When we “deny” Jesus, and we do when we sin, Jesus looks upon us with compassion. He remembers we are just dust (Ps 103:14). When we sin, Jesus invites us to meet with Him in a personal, private way to resolve our “denial”. He doesn’t want us to remain in our sin and defeat. As with Peter, whose denial was forgiven, and who went on to serve Jesus greatly, Jesus will forgive us and we can go on to serve Him also. With Jesus failure is never final.