Have you ever heard someone say, "Why has this happened to me?", and maybe follow up with "I've tried to live a good life, and honor God, and pray; why me???" Of course you have. I doubt anyone has ever failed to hear this spoken by someone else or themselves a number of times in their lives. It goes along with the old question: "Why does God allow bad things happen to good people?"
Both of these indicate a very basic misunderstanding of Christ, and His purposes here, and his teachings. It implies that the speaker thinks they're someone so special, or so "godly," that they believe they should be exempt from the trials that are so common here on earth. Nothing could ever be further from the truth! God doesn't give us challenges in life as a punishment, but as an impetus for us to learn more, believe more deeply, and SHOW Him what we REALLY care about and believe in. It's really just that simple.
Just once, I'd like to hear someone say, "Why NOT me?" Now THAT is a question that's MUCH more fitting for a Christian. But I won't be holding my breath until I hear it. For that's just the way we humans have been created - just potentially good enough to find salvation, and just willful enough to walk away from it, at least try to for brief intervals. So if you ever find yourself asking "Why me?", just catch yourself, and smile a sheepish smile, and get off your duff and get up and address whatever it is facing you. Now THAT is what God really intends for us to do!