The short answer is simply that there are better and more accurate ways to gain knowledge of the world and our place in it. For the purposes of this essay though, we’ll just look at the flaws of theistic ways. First, a definition:
Theism is belief in the existence of a god or gods. In the West it has a more specifically monotheistic interpretation: belief in the existence of one God viewed as the creative source of the world and who transcends yet is immanent (IE: present) in it. Still, the monotheistic interpretation is a subcategory of theism. The actual number of gods is immaterial. Hindus, pagans and others who worship multiple gods are theists too.
So why do I reject theism as a valid worldview? Well, let's put aside for a moment the good or bad things people claim religion inspires; the purported redemptions and condemnations, the moral guidance or the skewing thereof; the assertions of superiority of this one over that one and all the other divisive little things theists do in the name of inclusivity. Let's just examine its validity as a worldview.
At one time it was the best view mankind had to offer. From the earliest times people looked at the world and wondered what made the tree give shade, what gave the fox its cunning, or why a rock chose the particular moment when someone was beneath it to fall off a ledge. They decided it was because everything, animate or inanimate, had its own will. The idea that spirits or god-force infuses everything survives in certain cultures such as some American Indian tribes and, if you don't mind stretching the point a teeny-weeny bit, those Star Wars fans who think "The Force" is something real.
As humankind's knowledge of the world expanded, religious ideas evolved to encompass what was known and offer explanations for it. Eventually, it was the turn of the monotheistic faiths that so many subscribe to today to come and offer their explanations for everything. The process involved in this evolution of ideas is fascinating but not within the scope of this essay. If you're interested though, Richard Dawkins goes into the subject pretty thoroughly in The God Delusion. For my purpose, I just want to make three points. The first is that humanity's knowledge of the world around it didn't stop expanding with the publication of anyone's holy books. The second is that there is absolutely nothing in anyone's holy books that arguably couldn't have been conceived of or known by people living at that time; so a claim of "divine inspiration" or "special knowledge" is definitely open to question. I'll explain the third point in my conclusion.
The accuracy of the first point should be self-evident. The second point requires a closer look though. The claim of divine inspiration is not unquestionable anywhere in the holy books I've read. Take what they say about morality for instance. The Golden Rule is revered in all three of the great monotheistic faiths, but the fact is, in some form or other, it common to just about every other human culture that's ever existed. So are general rules against lying, killing and stealing. Since it should be evident that no society can last long if rules like these aren't followed, isn't it possible that people could think of them without divine intervention? If you admit this is possible, then you have to decide which scenario is more plausible; that God(s) inspired and enforces moral laws or that men thought of them and claimed that God was enforcing them. There’s a social benefit in believing the latter even if it’s not factually true. After all, it's easier to evade a policeman's eye than that of an omnipresent god who’s watching you and taking notes on your infractions. It's actually irrelevant whether or not the people who wrote the holy rulebooks thought they were divinely inspired. It only matters if their followers think so.
And we needn't examine whether all these rules are truly moral or not; or whether they sometimes contradict what we think is moral today, such as whether it's an unalloyed good to be willing to kill your own child to please God as Abraham and Jepthah were; or whether God was making some profound moral point by sending a bear to kill children who were teasing a bald man. These things may not help the case for God's goodness but they don't say anything about who wrote the Bible either: divinely inspired men or just men. Extraordinary claims require extraordinary evidence to be considered seriously.
So where is the extraordinary evidence for divine inspiration or special knowledge?
Where in the Bible does Jehovah say, "no, no, no, King Hiram! 3 is not the best value to use for pi when you build my temple. Use 3.14159 and the structure will be more pleasing to me." If God had given the value of pi to five or more decimal places, that would have shown special knowledge unavailable at the time. As it happens, the Egyptians already had calculated pi to two decimal places but the supposedly divinely inspired Hebrew who wrote about the First Temple wasn't even aware of that. Similarly, wouldn't it be nice if Jesus said, "Hey, I raised Lazarus from the dead but here's a miracle you can perform even when I'm not in town; a cure for cancer." And isn't it too bad that the angel Gabriel never whispered to Mohammed, "Hey, Mohammed! Here's a real revelation for ya! Mass is just a special state of energy and you can determine the relationship between them with this simple formula, E = M*C (squared)." Unfortunately, there is nothing in any of the holy books that could not plausibly originate from the minds of people of that time. Even the verses that some claim predict future events, such as the Jewish Diasporah as Deuteronomy 28:64 and Luke 19:43-44 are supposed to do, aren't written with the kind of specificity one would expect from an all-knowing deity? If they were, they might read, "66 years after the Savior's birth and again 132 years after it, the Jews will rebel against their Roman overlords, be defeated after terrific struggles and be scattered across the face of the Earth. Not until 1,948 years after the Savior's birth will they have a homeland again." (author's note: most of these examples were taken from or inspired by Sam Harris's wonderful little book, Letter to a Christian Nation. I recommend it for its concise, easy-to-read explanations of most of the critical thinking vs faith arguments.)
Finally we come to my third point. Despite the fact none of monotheism's holy books can be unequivocally shown to originate anywhere other than the minds of people of the times they were written, each claims to be the repository of absolute truths. The effect of this is a tendency to freeze that time's worldview into dogma and retard the acceptance of any new knowledge that's at odds with it. It skews understanding as people of faith try to pound the square peg of reality into the round hole of their dogma. Almost all the social, material and scientific progress of the world has been held back rather than assisted by theists. It isn't just Galileo's sun-centered view of the solar system or Darwin's theory of evolution that they've rejected and tried to suppress; it's Edward Jenner's smallpox vaccine, Benjamin Franklin's lightning rod, emancipation of women and a whole host of other things. These aren't the only reasons I reject theism as a valid worldview. They are however, a few of the major ones.
“Reason must be deluded, blinded, and destroyed. Faith must trample underfoot all reason, sense, and understanding, and whatever it sees must be put out of sight and ... know nothing but the word of God.”
-Martin Luther (1483-1546)