This is a question that most believers are asked at one time or another. Most recently, it was posed by Invictus at In Mala Fide, and it is a question that I believe always merits a direct answer. It is a question to which there are many different possible answers, and many different correct answers. Why I believe is probably not why someone else believes, even in the unlikely event that we happen to believe exactly the same thing, whether our belief is religious, political, or scientific in nature. In this case, the question was focused on religious belief, and I answered accordingly.
Why am I a Christian? Because I believe in evil. I believe in objective, material, tangible evil that insensibly envelops every single one of us sooner or later. I believe in the fallen nature of Man, and I am aware that there is no shortage of evidence, scientific, testimonial, documentary and archeological to demonstrate that there is no individual who is perfect or even perfectible by the moral standards described in the Bible.
I am a Christian because I believe that Jesus Christ is the only means of freeing Man from the grip of that evil. God may not be falsifiable, but Christianity definitely is, and it has never been falsified. The only philosophical problem of evil that could ever trouble the rational Christian is its absence; to the extent that evil can be said to exist, it proves not only the validity of Christianity but its necessity as well. The fact that we live in a world of pain, suffering, injustice and cruelty is not evidence of God's nonexistence or maleficence – it is exactly the worldview that is described in the Bible. In my own experience and observations, I find that worldview to be far more accurate than any other, including the shiny science fiction utopianism of the secular humanists.
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I don't concern myself much, if at all, with the conventional extra-biblical dogma that you describe and in which many Christians believe. I am dubious about the concept of the Trinity as it is usually described, do not await an eschatological Rapture, have no problem admitting that the moral commandments of God are arbitrary and readily agree that the distinction between the eternally saved from the eternally damned appears to be more than a little unfair from the human perspective. On the other hand, I know that evil exists. I have seen it, I have experienced it, I have committed it, and I have loved it. I also know the transforming power that Jesus Christ can exercise to free an individual from evils both large and small because I have seen it in the lives of others and I have felt it in my own life.
Now, ever since St. Augustine wrote his Confessions, it has been customary for Christians to exaggerate their sinful pasts; Augustine was hardly the Caligula that he portrayed himself to be. I find dramatic personal histories to be tiresome in the extreme, so I won't say more except to note that as an agnostic, I enjoyed a sufficient amount of the hedonistic best that the world has to offer across a broad range of interesting and pleasurable experiences, only to learn that none of it was ever enough. It may amuse you to learn that one woman who was acquainted with me prior to my becoming a Christian happened to learn about "The Irrational Atheist" and wrote to me to express her shock: "The fact that you wrote this book proves there is a God."
And apparently, a God with a sense of humor, no less. Now, there's no reason this would mean anything to you or anyone else who was not familiar with me then. But it meant something to that woman, just as an observable transformation in one of my close friend's lives made a distinct and important impression on me.
I certainly do not deny the experiences or revelations of those who subscribe to other religions. I merely question the specific interpretation ascribed to them by those who lived through or received them. After all, the Bible informs us that there are other gods and that those gods are capable of providing various experiences at their discretion, within the limits to which they are subjected by the Almighty. In addition to Economics, I majored in East Asian Studies in college and have spent a fair amount of time reading the sacred texts of various religions, including a few fairly obscure ones. I have yet to encounter one expressing a religious perspective that can be legitimately confused with the Christian one, nor, in my opinion, do any of these alternative perspectives describe the observable material world as I have experienced it as well as the Christian one does. And is it not astonishing that an ancient Middle Eastern text is quite often a better guide to predicting human behavior than the very best models that the social sciences have produced despite having an advantage of two thousand more years of human experience upon which to draw?