The question seems to really be about why one should believe the Abrahamic religions, rather than belief systems in general. Since Goblin asked, here's a stab at providing a few predictions they (particularly Christianity) make that turn out to be correct.
The term original sin was first coined by Augustine around 400, but Christians point to their scripture as the source for this doctrine. The general idea is that each of us shares a sin that dates back to our origin, and whose effects persist throughout our mortal lives.
One prediction that this theory makes is that all people, no matter how wise they are inherently, will make bad decisions. This of course disagrees radically with much of earlier Greek thought. Take for example the "Gold Soul" people in The Republic: Plato (through the voice of Socrates) claimed that as long as we put this small group of people in charge, we could achieve a perfectable society.
Which of these two models do we think is right? Most well functioning governments today are based on a system of checks and balances, which seems necessary if and only if the doctrine of Original Sin is true.
Benefits of a Virtuous Life
One tenet of the Abrahamic religions is that to be happy, it is necessary to be virtuous. Specifically, the virtues are:
- Justice - must give to each what he is due
- Prudence - must know how to be sensitive to a particular situation
- Courage - must persist in Justice/Prudence despite outside forces
- Temperance - must persist in Justice/Prudence despite interior forces
- Faith - once some knowledge has been obtained, persisting in certainty in that knowledge despite doubts (usually applied to knowledge about God). Not to be confused with superstition or credulity.
- Hope - Keeping in mind some goal that is possible but uncertain (in religious settings, the goal is usually Heaven, but can be applied to other things as well)
- Love - Acting for the good of others for their own sake
Before Christianity existed, philosophers wrote about the first four virtues (the Cardinal Virtues) extensively, and how they were required for a happy life. Experience also shows that a person can be made happier by following these. As an example, we all seem to know someone whose intemperance, manifested as substance abuse, has been made unhappy.
Faith is less obvious, in part because it is colloquially used to mean something different than what it means in a philosophical/theological setting. CS Lewis used the following analogy: when a surgeon tells you that you need surgery, it is easy to intellectually understand that. Faith comes in as the anesthesiologist puts on the mask to put you under. As I summarized above, Faith is persisting in knowledge of something despite doubts and seeming contradictions. Without this persistence, progress is obviously impossible: if one keeps changing one's mind, nothing ever gets accomplished.
Hope also means something different in a technical sense than is often used colloquially. Many of the great moral advances fall under the category of hope, that is, they were things that were desired, possible, yet uncertain. Just a few examples: the Civil Rights movement, the over-throwing of Apartheid, the defeat of the Nazis. Through this lens, it is clear that hope is a great motivator for good and creates happiness.
Love is a bit more obvious. The Iterated Prisoner's Dilemma demonstrates intellectually that acting selfishly can make everyone worse off in the long run, but more personally many of us have experienced how our loving others makes us happy.
To summarize: the above tenets of Christianity show that their predictions tend to be true, and confirmed by common sense and personal experience. As one gets into details, there are necessarily lots of messy exceptions, but life is messy after all, and a Theory of Life would necessarily be just as messy.