What best accounts for these facts? Hallucinations do not occur in mass settings. Mistaken identification is not plausible for family members and close friends. Wishful thinking is not reasonable for those who sought to persecute rather than follow, or for those who never believed Jesus' teachings during his life. Seeing that the cumulative case points to the fact of the Resurrection can be a powerful way to support the faith.
Many who argue against these claims do not do so on the basis of abductive reasoning; they don't assess the piles of evidence to determine what other reasonable inference would better fit the known facts. Instead, they begin with the presupposition that miracles cannot occur. Consequently, any explanation of these events which rely on the miraculous is rejected out of hand. The case is lost before it is even considered.
In short, many argue that relying on the possibility of a miracle is simply an admission of ignorance. If you can't establish how the miracle occurred, they argue, you should not be able to rely on it.
This challenge to provide an explanation for the "best explanation of the facts" is clever but misplaced. There are many circumstances in which we can know something to be true, or to work, without knowing how it is that this is so. Take reason or a sense of fair play, for instance. I make use of these things even though I have no way of explaining how reason works, or why I should rely on it. Consciousness is another example: in operating rooms around the world, anesthesiologists make use of drugs that can put people "under" and then restore them to consciousness without knowing how it is that this occurs. They understand the effect these drugs have on the cellular level, and they can measure differences in brain wave activity, but understanding how a grouping of brain cells goes from conscious to unconscious and back is still beyond them. Though not usually considered as such, consciousness and reason are themselves "miraculous" - no sufficient naturalistic processes can account for them.
So, if the evidence that a man was put to death and then appeared again in a re-animated and enhanced body is sufficiently credible, then the fact that we cannot current "explain" how it occurred does not prove that it did not occur. Consider for a moment the many medical "miracles" that have occurred. There are countless cases in which a disease process stops, or reverses, for reasons that are simply not clear, at least at present. As knowledge and technology advance, some of these miracles will be explained through naturalistic mechanisms. But how can the skeptic possibly know that this will always be the case? Would this not require perfect knowledge on his part, in order to know with certainty that departures from the laws of nature can never occur?