Conflict of method
Jerry Coyne argues that religion and science are incompatible because both make contradictory claims about reality and use different methods to support their claims.
Science uses reason, observation, and experimentation to make claims that are independently verifiable. Religion relies primarily on revelation and tales of miracles that cannot be independently verified.
Science guards against confirmation bias through peer review, independent verification of falsifiable hypotheses, and fostering a culture of scepticism. Religion encourages confirmation bias by relying heavily on subjective faith experiences, unfalsifiable claims, and discouraging a culture of doubt.
In short, scientific hypotheses undergo rigorous scrutiny before being accepted as provisional truths whilst religion makes absolute truth claims that are unevidenced and unverifiable.
Conflict of outcome
The upshot of such conflicting methodologies is that science and religion make contradictory claims about reality that are incompatible. Science has a history of proving religious claims wrong and forcing theologians to conveniently rebrand obvious scriptural falsehoods as metaphors.
Examples include the debunking of the Adam and Eve myth through evolution or the debunking of the young-earth biblical view with the scientific discovery that the earth is at least 4.5 billion years old. In the end, despite its confident claims, religion is incapable of producing any objective truths at all, only speculative and often unfalsifiable conjectures.
Why the incompatibility matters
Despite its waning influence, religion still has a strong influence in countries such as the US or in the Middle East.
A religious worldview impedes humanity's progress. The belief that all will be well in the next life or that the end times are near can reduce people's incentive to take action to improve our world by tackling issues such as climate change, disease prevention, or social inequality. Karl Marx was right in saying that religion acts as the opium of the people.
A religious outlook can impede scientific curiosity and progress by making people more concerned with an imaginary afterlife rather than tackling problems like consciousness or understanding the existence of the physical constants of the universe. Coyne asks us to imagine how better off the world would be if the intellectual acrobatics and logical rigour of theologians were channelled towards better ends.
Most importantly, religion can cause a lot of harm. Misogyny, mistreatment of homosexuals, opposition to stem-cell research, opposition to euthanasia, opposition to disease-preventing vaccinations, negligence towards climate change, medical neglect in favour of prayer, child mutilation through circumcision, corporal punishment for benign acts, and perhaps most importantly, the fostering of division between people through religious or sectarian conflicts.
What to do?
Coyne cites several studies to suggest that there may be a link between the social well-being of a society and its religiosity. The more socially dysfunctional a society, the more likely that its people will seek consolation through religion. So our best strategy in reducing religiosity might be to improve the well-being of societies by, for example, ensuring free universal medical care and promoting social welfare programs in general.
Coyne ends by noting that it is time we stopped giving religion the special deference that it enjoys.
"It is time for us to stop seeing faith as a virtue, and to stop using the term "person of faith" as a compliment. After all, we don't call someone who believes in astrology, homoeopathy, ESP, alien abduction, or even Scientology a "person of faith", even though that's precisely what such people are."
Comparing religion to astrology will doubtless offend people but I think Coyne makes a compelling case in his book for why such a comparison is not so off the mark.