I have always had an affinity for the Apostle-Prophet Simon Peter. When I was little, my mom had a music sampler which included one song about Peter's denial of Christ, and the lyrics framed Jesus' phrase "Thou shalt deny me thrice" as a commandment rather than a prophecy. In other words, Peter was saying, "I won't leave your side, I'll die with you," and Christ responded, "No, you must deny that you know me and leave me alone for this work to be completed."
Now there isn't really anything doctrinal to support this. I have seen a couple of talks that mention this as a possibility (of course, I can't find any right now), but most of the general authorities talk about Peter's denial in traditional terms (a couple of great talks on that here and here!).
But even within that traditional viewing of Peter's experience, I feel so much for his situation. He didn't want to let Jesus go. He didn't want to leave his side. He was determined to remain loyal, even to death, which is evidenced by his attack on the party who came to apprehend Jesus. But at that point, Jesus detained him, healed the servant's ear, and explained that all of this had to happen to fulfill the scriptures (Matt. 26:51-54). It wasn't until then that Peter left Jesus' side, and thereafter came the denial. It didn't happen until after the option to fight for his Friend--the first inclination of this impetuous disciple--was taken away. And so I am sure the tears that came were doubly bitter because not only had Peter denied Christ, he still had to watch, helpless, as Christ was abused, humiliated, and murdered. Such a confusing and trying time! But from that trial Peter rises above this to become a more-than-valiant advocate, and eventually does give his life for Christ. What an amazing man!