Since the resurrection comes as a direct result of the Atonement I went to study about it. I found the first part of the "why" while reading Tad R. Callister's "The Infinite Atonement" as follows:
“Everyone who has had a mortal body will be resurrected – the righteous, the wicked, even the lukewarm – for the resurrection is universal. It is a free gift to all men regardless of their righteousness. But why? Why the disobedient, the scoundrel, the atheist? Is it fair? It is. Adam brought physical death into the world through his transgression and thus transmitted his mortal nature, the seeds of death, to all living creatures without any action on their part. They did nothing to merit death in their earthly sojourn, and so in return, the Savior restored immortal life without any redemptive action on the part of man. The plan is fair and just and merciful.
This was so relieving to me because I then realized that since nothing we did or could ever do warranted our death in the first place, it makes the resurrection completely justified and that much more real for everyone! What a beautiful and comforting truth!
The how came next. I was reading one day in 2 Nephi 9:12,
"...wherefore, death and hell must deliver up their dead, and hell must deliver up its captive spirits, and the grave must deliver up its captive bodies, and the bodies and the spirits of men will be restored one to the other; and it is by the power of the resurrection of the Holy One of Israel.
But the the Spirit nudged me to focus on the word "power". What's one of the first things that comes to mind when talking about divine power? For me, it was "priesthood". I had been looking at it from the wrong perspective, thinking of the event of His resurrection as the one and only catalyst for our own. What I was missing was that the key word is power. Specifically, priesthood power.
It was so simple and I had overlooked it by going beyond the mark so many times! The Savior reclaimed His body by the power of His priesthood - also referred to in 2 Nephi 9 as the power of the resurrection - and we reclaim ours as well by that same power.
As Elder Callister teaches, God's "plan is [indeed] fair and just and merciful."
I love my Savior and I am thankful for His loving kindness and the beauty and love of His gospel and His plan for us, that each of us will receive totally perfected, flawless physical bodies, conducive the eternal joys for which we qualify ourselves in this life.