The standard definition of Atheism is that it is a disbelief in the existence of God.
The problem with this definition is that it depends on a precise definition of the word "God". An atheist can "disprove" the existence of one particular type of God, but then some religious opponent will suggest the existence of some different type of God, one whose existence is not disproven by the atheist's first argument.
To avoid this difficulty, I prefer a definition of Atheism which doesn't even mention God, but which I think sums up what most people who call themselves "atheists" believe about religion:
The contents of religious belief systems do not tell us anything useful about the nature of reality.
In other words, Atheism is not so much a disbelief in God, as a disbelief in religion, and to be specific, a disbelief in the contents of the more popular religions.
Armed with this definition, we can consider some of the major categories of propositions contained within religious belief systems, and why it is that atheists disagree with those propositions.
A major doctrine of Christianity, and of some other major religions, is that one or more people wrote down some historical accounts of actual events, or of information imparted to them by a divine being, and that it follows, given that the person wrote it down under some particular circumstances, that those writings are all true. Often there is assumed to be some "proof" that occurred at the time which proved the truth of these writings, and sometimes these proofs are themselves described within the writings.
The main refutation of this claim is that:
Modern biblical scholarship has shown that not only do people make stuff up, but sometimes the making up is an on-going process, where one person takes an existing made up story, and then makes up more stuff, to create an "improved" version of the same story. (And you don't have to be a scholar to see this – just read some of the "parallel" versions of stories that occur in the Gospels in the New Testament, and try and give a sensible explanation of some of the similarities and differences that you find.)
Morality is a major theme in religion. Two claims made by (or in association with) many religious belief systems are:
The questions of exactly what morality is, and how moral "truths" are determined, are questions that are perhaps not yet fully answered by a scientific understanding of human nature. (And it's worth mentioning that human beings are very complicated, and there are lots of things about human nature which are not well understood, so this difficulty is not peculiar to morality.)
But it is possible to give some straightforward refutations of the two propositions given above.
Firstly, there are modern Western countries where a significant portion (e.g. 30% or more) of the population lacks any serious religious belief, and these countries have not collapsed into a swamp of depraved immorality.
Secondly, there are some aspects of our modern shared view of morality which are not mentioned within popular major religions, or if they are, it is implicit that those aspects of morality were unknown to the authors and inventors of those religions.
Two major examples from the Christian Bible are:
Sentient beings play major roles in religious belief, including, but not necessarily limited to the following:
According to modern physics, our basic description of reality consists of the Standard Model Lagrangian and the Einstein Field Equations (which despite the plural syntax, is just one equation when written in tensor form).
Of course to fully understand modern physics, you need to know what these formula mean, and what mathematics lies behind them. There's also the issue that these descriptions and their associated theories are known to be incomplete, and they contradict each other, although for all observations we can make which depend on both theories together, the observations can be described in terms of Special Relativity, which is a limiting form of both theories. It is presumed, at least by those scientist who are optimistic that science can one day explain "everything", that the "true" complete Theory of Everything will consist of some single mathematical theory such that those two theories (i.e. the Standard Model and General Relativity) are limiting forms of that one single theory.
Regardless of all these caveats, we can observe that neither of these theories makes any direct reference to the concept of sentience. In as much as sentience is something that exists in the real world, it is a consequence of these more basic descriptions of reality, and there is no scientifically observed consequence of the behaviour of sentient beings which contradicts either description. Which, among other things, tends to rule out the existence of all different types of sentient beings in the list above, except for the first one.
The concept of sentience is closely related to the concept of magic. We can define magic as follows:
Magic is when a sentient being causes something to happen because they want it to happen, and it can be demonstrated that there is no conceivable physical explanation for how it happened (so the only explanation of why it happened is that the sentient being wanted it to happen).
There is the more general concept of the supernatural, but most of the supernatural phenomena that people are interested in can be understood as examples or demonstrations of the more limited concept of magic that I just defined.
Almost by definition, the existence of magic is contradicted by the scientific worldview. Of course there have been scientific studies done of various forms of magic (which generally get called ESP when they are being studied scientifically). Although not always stated explicitly, there is a general assumption that if science could verify the existence of magic, then our basic understanding of reality would have to somehow be revised so that the sentience of sentient beings was resuscitated as a basic explanatory concept within a scientific theory of everything.
As it happens, scientific studies of magic have not resulted in any convincing demonstrations of the existence of magical phenomena. Which means we can stick with physics as the basis of our best understanding so far of the nature of reality.
Because religions tend to make broad statements about the nature of reality, and so does science, arguments about which is more correct tend to become discussions about questions that science has not yet answered.
To deal with these questions, someone arguing a scientific point of view might be tempted to invoke a theory which is not yet proven, or a controversial interpretation of an existing theory.
On the one hand this can lead into dubious territory, for example one might assert that M-Theory is a likely description of the nature of reality, which explains all physics, and given such an assertion, one could then conclude that all religious beliefs are proven wrong (presumably by showing that they would definitely contradict M-Theory if they were correct). However M-Theory is an extension of String Theory, which has been famously described by Peter Woit as "not even wrong", and nobody has come up with any hard evidence in favour of either theory since Peter Woit made that statement. Which makes it a rather dubious basis for a refutation of religion.
On the other hand, there may be some unsolved scientific questions, which are often raised by those arguing in favour of religion, which do require an answer of a form which is at least potentially controversial. Even the invocation of M-Theory is to solve the so-called "fine-tuning" problem, and M-Theory is just one possible justication for applying the Anthropic Principle as an "explanation" of how life has originated in the Universe, even though such an origination might be a priori extremely unlikely. I think that there is a lot of confusion around the Anthropic Principle, some of it around whether or not we need the Anthropic Principle to explain anything, which is a different question to the question of whether it is OK to invoke it if indeed it is necessary to do so. (In other words, proving that the Anthropic Principle is unnecessary to explain a particular observation is not the same thing as proving that the Anthropic Principle itself is wrong.)
For a more minor example of controversial scientific arguments against religion, consider my analysis of the thermodynamics of evolution by natural selection, where I conclude that to "explain" evolution thermodynamically, you really do have to believe that entropy can spontaneously decrease within a closed system (but only by a very, very tiny amount on each occasion). If you read the many "refutations" of the Creationist assertion that evolution breaks the Second Law, you will find that none of these refutations properly deals with the issues raised in my analysis (of course the Creationists don't help because they fail to clarify the strongest form of their own argument, although as I point out in my analysis, Granville Sewell comes pretty close).
It follows, given the nature of these controversies and others, that even Atheists with scientific worldviews can disagree as to what is the best way to refute all the different religious beliefs that religious people believe in.
In the end, I can only speak for myself, and explain why it is that I don't believe in the things that religious people believe in.
(And yes, just in case you weren't sure, the title of this article is an allusion to Stephen Hawking's new book, which apparently isn't mostly about God or M-Theory, but those seem to be the topics in his book that were deemed most newsworthy.)