Many intelligent people don't believe in God because it would acknowledge that there exists something smarter than they are. We all like being in charge.
Most studies show a strong correlation between education and atheism: the more education a person has, the less religious they become and even less theistic. Some religious theists, seeking a way to attack atheism, try to use this against atheists by claiming that atheists' intelligence is a reason for their disbelief not because they really do know more, but because they are too arrogant. Atheists, according to this myth, don't want to admit the existence of a god smarter than they are.
This myth is remarkably similar to the popular Christian claim that atheists simply don't want to accept divine sovereignty or rule over them. What occurs here is an attempt to attribute a person’s disbelief to a desire to evade what they don’t like about God. The first thing to notice about this argument is that it is a logical fallacy, known as the Genetic Fallacy.
All that is happening here is that the theist is making a claim about why a person is an atheist and then attacking that motivation. This does not, however, say anything about atheism itself. No reasons are given for thinking that atheism is an unreasonable position and no reasons are offered for believing in any gods. The Genetic Fallacy is a type of ad hominem argument because it attacks the person who holds the position, not the position itself.
Aside from the fact that this claim is fallacious in its reasoning, it is also erroneous in its premises. Contrary to what some religious theists may think, atheists accept the existence of smarter people all the time — for example, scientists who know more about physics or engineers who know more about how things are put together. I've never encountered any atheists who even suggested that they thought no one in the world was smarter than they are — and that includes even the very smart atheists.
Furthermore, even if some god exists, who is to say that it is necessarily a very smart god? People who have been raised in traditional monotheistic faiths will automatically assume something like "omniscience" whenever they hear the label "god," but if we're honest we have to admit that there is nothing about the concept "god" which implies any level of intelligence.
If any god exists, it might be more or less intelligent, more or less knowledgeable, more or less creative, etc. Such a god might plausibly know more about matters like physics, but not as much about matters like falling in love or how to maintain a relationship — after all, where would a god obtain such knowledge, anyway? It's thus possible for an atheist to become a theist by accepting the existence of god without also believing that this god is very intelligent.
Therefore, the argument for rejecting atheism because of the claim that atheists disbelieve in God in order to avoid admitting the existence of a being smarter than them is both invalid and unsound. It is invalid because the reasoning process is faulty — it commits a logical fallacy, so regardless of the truth of the premises, the conclusion does not follow. It is unsound because the primary premise is clearly incorrect.
Atheism cannot be reduced to mere intellectual arrogance in this manner. Atheists are not inherently arrogant about their own intelligence, which means that they could accept the existence of an intelligent god alongside the existence of intelligent people. Gods are not necessarily intelligent, which means that their alleged intelligence could be rejected even while believing that one exists.