The most important reason to question believing in God or indeed believing anything is the simple fact that truth should matter. So long as truth matters to you, then you should care whether what you believe is true or not. If you care whether what you believe is true or not, then you should be willing to question what you believe and subject it to critical scrutiny. Testing what you believe against logic and evidence is the only way ensure that what you believe is more likely true than not. If you won't question what you believe, then you can't care much about truth.
Skepticism & Critical Thinking are Vital Habits
Skepticism and critical thinking are not tools that can or should be used randomly or inconsistently. They are difficult skills that can be challenging to apply, especially with favored or popular beliefs. This is why these skills flourish best when they become habits. Making them habits allows us to use them more often and more effectively. If you really are going to develop habits of skepticism, though, you have to include theism and religious beliefs among the subjects you apply the skills to. That remains true regardless of whether any sort of god or gods exist or not and regardless of whether any religions to true/valid or not.
Religion Should Not Be Privileged
It's popular to privilege religion and theism in a variety of ways, including by exempting them from the sorts of challenges, questions, and criticisms that are regularly applied to other opinions and ideologies. This tendency is completely inappropriate because neither religion nor theism deserves to be exempted from critical scrutiny or probing questions. No one objects to questioning other opinions, so why object to questions here — unless, of course, one's belief is insecure and one suspects that the questions might reveal that the belief if flawed or even wrong?
Religious Leaders Should Not Be Privileged
So many believers tend to accept whatever their religious leaders tell them about gods, faith, scripture, heaven, etc. No religious leader is perfect, though, so there's no good reason for not questioning their claims. Religious leaders are every bit as human and fallible as their followers. They don't seem to be any smarter, on average, and many aren't even necessarily any better educated. Accepting their claims about the supernatural without question only feeds their egos and their power; it doesn't serve the interests of truth.
Religious Claims Have Been Proven Wrong So Often
The number of religious claims that have been proven wrong, if not absurd, is so large that it probably isn't even possible to create a list. Even religious theists will agree that if we were to create a list of all religious beliefs ever held by humans, most would be wrong. Given this incredibly poor record, how reliable can we treat the relatively small number of claims that are still being disputed? Of course, this isn't proof that they are definitely wrong, but it does suggest that religions do not produce reliable, accurate information and knowledge. That should give us good reasons for skepticism.
Not Everyone's God Can Exist
Large numbers of people have believed in a god or gods over the millennia, but they've all believed in different gods. It's not possible for them to all exist which means that most of these beliefs (if not all) have been wrong. Maybe you happen to be one of the few who happen to be right and happen to believe in the only god or gods on that long list which actually exist, but the chances of that aren't very high. This should be a good reason to ask hard questions about theism and religion. To not ask those questions would be incredibly arrogant.
God's Job Description Has Been Shrinking
Anyone who looks at the history of Western theology over the past couple of centuries will notice that God has been given less and less to do. At one time God and other supernatural beings had responsibility over diseases, but now they belong to the realm of medical science. At one time God had responsibility for the weather, but now it's a matter of meteorological science.
The more we learn about the world, the more things that become the subject of scientific inquiry — and the less authority the supernatural is given. At no point have we learned anything that has expanded the scope of responsibilities for any gods or any alleged supernatural beings; at no point has anything been moved from a scientific field to theology. And there's no reason to think that will happen in the future, either.