Why would someone believe the bible is the inerrant word of god? Reduce this question to "why would someone believe something that is imaginary"?
I'm sure this is covered in depth by others (Shermer?), but I'm always struck by just the raw numbers.
First, if measures of IQ are relevant, half the people in the world are of below average intelligence. We shouldn't describe these folks as not bright ... but it's a statistic that can be verified to reasonable precision. We understand that 68% of all people are within 1 standard deviation of average (100 IQ), so 34% are between 100 and 116, and another 34% are between 100 and 84. The other 32% that are beyond one standard deviation from the norm are probably evenly split ... so 16% above 116 IQ, and 16% below 84 IQ.
Second, some people are gullible. Not unintelligent, just uncritical, overly trusting. I have no idea how you'd measure this population, but we all know people who will believe things without examination of the facts and logic behind the assertion.
Third, some people are prone to being lead. John Dean, in his critique of political conservatism Conservatives without Conscience asserted that approximately 20% of the population is easily lead by other people. This "Right Wing Authoritarianism" does not mean right wing politically, but right wing on the personality spectrum, as noted by Robert Altemeyer.
Fourth, we are fascinated with mystery and secrets - being privy to knowledge that others don't have, and to which we can claim authority, and gain notoriety and respect.
Fifth, some people don't have the time, resources, or education to find out and understand what many now consider fundamental knowledge - the age and size of the universe, the number of stars and planets that exist, simple chemical processes that produce the precursors to carbon-based life, and do so every minute, every day every millennia, and in places wholly unimagined as few as fifty or sixty years ago (outer space, deep sea vents, deep inside the earth). Evolution.
Sixth, some people are fearful. Maybe fearful of modernity, or fearful of uncertainty, or fearful of others that are foreign to them - again, here I am without statistical support, but I know, and you know, that some people are afraid of reflecting on themselves and this world, its possible genesis, the meaning of their lives, what death means.
There are large cohorts of the population who, through one or many of these (and others that I haven't enumerated) constraining factors might be prone to believe weird things ... religion for example. Combine this with the segment of the population that are motivated (for whatever reasons) to assert things that are untrue, whether or not they believe them. You can begin to see P.T. Barnum's maxim at work, but on an immense scale.
Go back in time 2 or 3 thousand years, and compound these factors by the relative isolation, tribalism, lack of developed social structures and illiteracy of people in the world, and we have conditions that are ripe for the flourishing of religion. Most people in the pre-BCE middle east were not literate. Estimates are that up to 99% could not read or write. A select few could, and these people could secure influence for themselves by recording and promulgating ways of thinking that only they were privy to.
Is it any wonder that superstitious thinking became the norm three thousand or more years ago? Is it any wonder that it persists today?
More importantly, isn't it time to outgrow this superstitious thinking?