Your inquiry is appropriate since I have, throughout this homepage, indicated many reasons why theism continues to flourish.
Consequently, it makes sense to deal with the question on its own merits.
It is not a simple task to explain why, since the so-called age of enlightenment, theism in its many forms has survived the onslaught of science, philosophers, and non-believers and in fact has flowered in the form of many sects like weeds in a meadow.
In the polytheistic period, gods filled every nook and cranny of the universe, and, given its pre-scientific era, it is understandable that such beliefs took and held root.
But that period laid the foundation for the present tenacious hold theism has on the world.
The roots, like those of creeping vines, are deeply embedded.
And though, on the surface, they may be pulled out and destroyed, the broken remains, however small, merely rejuvenate and spring forth with renewed vigor.
So it is with theism and theistic religions.
But there is a caveat, a portent of the future: there was a time when almost everyone believed in some kind of a god or gods.
With the advent of science and greater insight into the nature of things, however, there is now about 20% of the world's population that does not accept the existence of Supreme Beings, and that does not include those "wobbling on the fence."
As for the "well-educated" and a handful of scientists who claim to believe, it is apparent that they never were able to overcome the thorough conditioning to which they had been subjected.
Despite the teachings of science, philosophy, non-believers, a handful of atheistic popes, "fallen" priests and the anti-theistic writings of such great minds as Epicurus, Bertrand Russell, Albert Einstein, George Bernard Shaw, Friedrich Nietzsche, Karl Marx, Sigmund Freud, John Stuart Mill, H. L. Mencken, Joseph Campbell, Robert Green Ingersoll, Arthur C. Clarke and so many more it would take pages to fill, there are two fundamental reasons which underlie all others as to why theism has survived and is still flourishing.
(1) EXTREMELY POOR EDUCATION throughout the world.
The world does not EDUCATE its citizens.
Consequently, its mindset is controlled by ignorance, politics, greed, money, power, religions, economies, needs of the masses, celebrity, influence, conflict, competition, entertainment, ambition, etc., with REASON playing second fiddle to them all.
Learning to think CLEARLY, CRITICALLY, and ANALYTICALLY, i.e., RATIONALLY, is the most laborious of enterprises.
Few have the gumption to engage in it and governments don't insist that it be emphasized.
Essentially, our governments SCHOOL and TRAIN us.
They prepare us for filling the employment needs of the business world, for financially supporting ourselves, and for learning the social amenities needed for human relationships, filling our minds with facts and information (so much of which are false) and NEGLECTING TO TEACH US TO THINK ANALYTICALLY--the definitive definition of the term 'EDUCATION'; i.e.; they rarely EDUCATE us.
To paraphrase Einstein: If one were to forget all the "facts" acquired while attending our institutions of learning, what is retained would constitute the degree to which one had been educated.
Too many of our teachers seem to be aware of or to emphasize the differences between:
belief and knowledge
rote memory and knowledge
claims and knowledge
convictions and knowledge
intuition and knowledge
common sense and knowledge
information and knowledge
perceptions and knowledge
concepts and knowledge
experience and knowledge
blind faith and knowledge
the illusion of understanding and understanding.
They fail to teach when language is our best friend and when it is our worst enemy.
They fail to teach that language, (i.e., meaning) in its multifarious and complex forms must never be confused with fact or reality.
They fail to teach that unverifiable claims have no epistemic value.
They fail to teach that language is about our perceptions and conceptions of the "world."
Such failure is evidence that of the six and a half billion people on earth, very few are subjected to true education which accounts for the ease with which the masses can be convinced that nonsense makes sense, i.e., that the ILLUSION of knowledge and understanding IS knowledge and understanding.
(2) MARKETING OF THEISTIC CONCEPTS:
Organized theistic religions' financial capacity (trillions of dollars over the ages) and/or
governmental control (in some nations) and political power [in America constitutionally protected and supported both by (indirectly used) public funds and freedom from taxation], to MARKET their theistic doctrines to the unenlightened masses of the world.
Given the above two verifiable facts, the people of the world are easy victims of the most heinous crime ever committed against mankind (See this issue above.): the PROMULGATION and MARKETING of theism.
The marketing process, completely devoid of evidence, is a pervasive drum beat, incessant and ubiquitous played by the people (often famous) we hold in high esteem and/or authority.
Theists disagree in their interpretations of the religious works of the world which explains the existence of thousands of different religious sects.
The numerous contradictions, incitements to atrocities, war, and pornographic acts, in the religious tomes of the world are either dishonestly never quoted, ignored, or explained away as metaphors.
The masses are not equipped to counter, not alone understand, theistic claims and arguments foisted upon the naiveté of the uneducated.
Miracles, for instance, are explained by theists as the work of God even though history has repeatedly shown that they are merely events not YET explainable by our embryonic sciences.
Part of the morally reprehensible marketing process is to usurp the principles of ethics and morality as having been decreed by God.
A belief in God is NOT A NECESSARY CONDITION for the existence of ethical and moral principles.
Millions of non-believers live their lives founded on such principles.
By cornering the market on morality, theists and theistic religions increase their power to manipulate our minds.
Theology is particularly marketed by Bible hackers (seeking power), bully-pulpit preachers, (also seeking power), some university theologians (in fear of losing their positions), and politicians (in pursuit of votes) -- the latter two in contradiction of their true beliefs.
Since there are no theistic genes, inasmuch as they do not encode ideas, and inasmuch as ideas are acquired through experience and the languages we use to discuss them, children are not born theists.
They are subjected to the conditioning processes from their day of birth to believe in an  incorporeal, UNKNOWABLE Supreme Being.
Theistic authorities manipulate us through all the functions and usage of language:   ceremonial, expressive, practical, aesthetic, logical ( and illogical), including all the emotional functions of language as well: the emotional language of fear, hate, joy, guilt, art, music (especially on both the pre-college and college levels), entertainment, promise of rewards (paradise in Heaven), threat of punishment (damnation in Hell) thereby controlling the thought processes and often the pocketbooks of the unenlightened masses.
Since we are a herd species, it is unlikely that the theists could achieve a joyous, good-feeling mentality of camaraderie among the masses without entertainment, art, and music, that is so necessary to organized religion and developing common beliefs.
For unenlightened people, it is vitally important that their blind-faith-held convictions be shared by others.
Theism has so extensively and insidiously infiltrated the speech patterns of the general public that even non-believers, myself included, cannot avoid using theistic terminology -- even if only as expletives.
It requires a long conditioning process to make one into a believer, but a religiously oriented world makes it easier to condition us.
Since we live in such a world, most people, including their teachers, believe in gods of one sort or another.
As some theist said: "Give me your child for ten years and I'll have him forever."
Once we are conditioned, uncountable sums of money are expended to reinforce that conditioning and to counter DEconditioning processes the main one of which is a true education (ANALYTIC thinking).
Believers do not analyze the theistic language foisted upon them by which they are taught and talk about "God" in the ILLUSION of understanding and knowledge.
They do not understand that no word has an inherent meaning and that they have been told what to mean by the words they use.
People fail to learn the difference between language that can be verified and language which cannot.
They are willing to accept the word of presumed authority figures or those held in high esteem without examining their areas of expertise.
Believers seek easy answers to what they do not and were not educated to understand.
Some people are born with the propensity to accept easy "solutions."
They are ably abetted by their ignorance of their own areas of ignorance and ignorance of the history of theism and religion and of the evolution of moral and ethical principles.
Such people are easy prey to those who for their own ends seek to control the lives of others.
The entertainment world, whether TV, literature, movies, whatever, is saturated with theistic language and concepts, feeding the socially and religiously imbued psychological needs to believe.
The use of euphemistic terminology gives the impression that something meaningful is being said when, in fact, gobbledygook is being served.
God can be known through faith, i.e., believe without evidence.
Science can't deal with matters of faith, i.e., implying knowledge is possible in the absence of evidence.
God is Spirit, (i.e., incorporeality), i.e., implying that nothing is something.
If God doesn't exist, where did the universe come from?, i.e., implying the universe needs a cause to exist but God does not (by definition).
God is all-knowing, all-powerful, all-whatever, i.e., implying God does not need a brain to know anything; eyes, to see anything; hands, to do anything; ears, to hear anything; etc.
Good people go to Heaven, i.e., implying there is a heaven without giving any evidence that it exists or what "life" as a bodiless soul would be like.
God will protect you, i.e., despite the preponderance of deaths, diseases, maiming, religious wars, hatred, and prejudices; volcanic eruptions, earthquakes, automobile accidents, birth defects, crimes, murders, broken marriages, dysfunctional families, unwanted pregnancies, weather related tragedies: floods, forest fires hurricanes; losses of home, property, jobs lifesavings, loved ones--to mention a few!
So long as our "educational" institutions make little sincere effort to EDUCATE rather than primarily SCHOOL and TRAIN the citizens of the world about the vagaries and vagueness of language, and so long as our religious institutions can persuade the citizens of the world to contribute to theists' financial coffers, and, thereby, they are able to MARKET those vagaries and vagueness of language as truth and knowledge, theism will flourish and thrive to the continued detriment of mankind.
See the next question related to one method of deceptive marketing.