Science and religion are not opposed to each other, as many people would like you to believe. They are sold as enemies because today's society likes drama and conflict provides bucket-fulls of it. But, it wasn't always that way. Even though there are fewer religious scientists nowadays (and I know some of them), centuries ago most people, including most scientists, were religious. Go far enough back and you'll find no scientists but rather natural philosophers. The influence of this is still felt today in the Doctor of Philosophy (PhD) degree that is the highest level degree awarded to both scientists and non-scientists.
"Philosophers", in the vaguest sense, are people whose curiosity gets the best of them. Their inquiry and questioning of any and all aspects of the world are what drives innovation and increases knowledge. The only limits that philosophers have are their abilities to logically argue for an explanation, generally relying on any of the various types of evidence and reasoning.
Scientific explanations go one step further - they must make testable predictions. For example, take Einstein's Theory of General Relativity. This theory essentially made Newton's Theory of Gravity more widely applicable. It added more detail and gave more precise results. Not only could General Relativity explain observations that Newtonian Gravity could not (e.g. no instantaneous influences), it also made predictions (e.g. the sun bends light from distant stars) that were later observed and confirmed to be true. This requirement ensures that scientific explanations can always be confirmed or re-evaluated and either tossed out or revised. The end result is explanations that are always improving.
Now, this brings us back to the initial point of the post: why "God" is a poor explanation. The problem with using "God" as an explanation for things is that it removes all of the things previously mentioned - inquiry and curiosity, reasoning and evidence. Even religious philosophers, like those who study the holy books, use these 4 main ingredients, if you will, of good argument. Let's consider what happens when the most important of those elements, inquiry, is removed.
Isaac Newton was a religious man, like most people of his time. That, however, never stopped him from asking questions (inquiry) and finding answers, not only about the physical world but also about the spiritual/religious one.
Everyone knows the story of Newton and the apple tree. Upon sitting under one on a sunny day, an apple fell from the tree and hit his head. This is what led him to his theory of gravity. But, what if instead of thinking more deeply about why apples fall from trees, he simply answered "because God makes them fall"? For him, this could have been a perfectly acceptable answer, but it wasn't satisfactory and doesn't require any further thought. If he had stuck with that answer, there might not be a theory of gravity, or at least, the theory would have come later by someone else.
So why does that matter? Apples will fall regardless of whether or not we have an explanation for why they do so. Remember before when I said that General Relativity expanded on Newtonian Gravity? If everyone used the "God" explanation, then there would be no theory of gravity or General Relativity. This also might not seem like a big deal, until you realize that one big application of General Relativity is GPS. Without knowledge of the effects described by General Relativity, GPS would likely be much, much less effective, if it even existed at all.
This game can be played with most "explanations" of our world, from physics to marketing. We have current society because there were philosophers who weren't afraid to follow their curiosity and ask questions, regardless of their religious ideology. Does that mean that "God" can never be an answer? Absolutely not. Sometimes, we just don't know enough to come to a satisfactory explanation. At this point, perhaps we can say "because God" - at least until someone smarter comes along. And, perhaps, there are some questions that will always remain in the "hands of God".
References and Further Reading (For inquiry!)
General Relativity by Harrison Prosper
Relativity and the Cosmos by Alan Lightman
Isaac Newton's Life by Isaac Newton Institute for Mathematical Sciences
Einstein's Relativity and Everyday Life by Clifford M. Will