Why can't science prove that gods do not exist?

In a Nutshell: Secularists and atheists promote a myth: Science and God are competing explanations. Atheists claim Science and God are competing explanations for such things as the origin of life and the origin of the universe. There is no need to cite God as an explanation, since science explains such things without the need for God. This reasoning commits what is known in philosophy as a category error because it confuses different categories of causation. The following two statements commit the same category error: "Living things are not caused by God, but rather, by natural processes." "Aircraft are not caused by people, but rather, by manufacturing processes." Put another way, in no way does it follow that merely describing how something was made amounts to an explanation of the cause for that something. Atheists here confuse scientific description with explanation. Bold declarations that "science explains things without the need for God" therefore amount to a category error.  Bo Jinn writes in Illogical Atheism: "In no way does it logically follow that something was not designed and built from the mere fact alone that that something could be understood scientifically. The law of gravity and Newton's laws of motion are to God and the universe what binary strings and electronics are to Alan Turing and the computer processor.  Function and agency account for two entirely different explanations as to how and why something exists. Aristotle explained this over two thousand years ago that everything in the universe could be understood in terms of: a formal cause, a material cause, an efficient cause, and a final cause. Science accounts for only two of those causes; the formal and the material. If we were to apply Aristotle's theory to the Harrier jump jet: The Harrier's material causes are the components from which it was constructed. Its formal causes are the laws of mechanics, aerodynamics and internal combustion. Its efficient causes are Ralph Hooper, Sir Sydney Camm and Sir Stanley Hooker [the designers]. Its final cause is to be flown in dogfights. Only the first of those categories of causes were open to the scientists in the story. Only the first two of those categories are open to science in the study of the universe." Atheism requires one to frequently ignore questions of efficient and final causation. As a further example of the category confusion which permeates atheist thought, atheists frequently cite natural laws as an alternative to God for explaining natural phenomena. But citing natural laws leaves us with the question of who or what enforces natural laws. In the theistic model, it is immediately obvious why matter follows natural laws: The same mind that creates matter (God's mind) also directs it. As Robert Boyle, the founder of modern chemistry, put it: "The nature of this or that body is but the law of God prescribed to it [and] to speak properly, a law [is] but a notional rule of acting according to the declared will of a superior." Or, as James Joule, the propounder of the first law of thermodynamics, for whom the thermal unit of the "Joule" was named, put it: "It is evident that an acquaintance with natural laws means no less than an acquaintance with the mind of God therein expressed." Or, as the knighted mathematician, physicist and astronomer Sir James Jeans put it in his book The Mysterious Universe: "There is a wide measure of agreement which, on the physical side of science approaches almost unanimity, that the stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than a great machine. Mind no longer appears as an accidental intruder into the realm of matter. We are beginning to suspect that we ought rather to hail mind as the creator and governor of the realm of matter. Atheism, however, is stuck with an "it just does" answer to the question of why matter so consistently follows natural laws. See this question for further arguments.