Science can destroy religion by ignoring it as well as by disproving its tenets. No one ever demonstrated, so far as I am aware, the nonexistence of Zeus or Thor, but they have few followers now.
Interpretation
Science challenges religious beliefs by simply disregarding them as well as by disproving them.
Arthur C. Clarke's quote suggests that the influence of science can diminish religious adherence by either ignoring religious claims or by providing evidence that contradicts them. He points out that while certain mythological deities like Zeus or Thor have not been proven to be nonexistent, their lack of followers today reflects the power of science to shift belief systems, leading people to abandon outdated religious notions.
In practice
In a debate about science and religion, one might quote Arthur C. Clarke to illustrate the shifting nature of belief.
Nowhere in space will we rest our eyes upon the familiar shapes of trees and plants, or any of the animals that share our world. Whatsoever life we meet will be as strange and alien as the nightmare creatures of the ocean abyss, or of the insect empire whose horrors are normally hidden from us by their microscopic scale.
As our own species is in the process of proving, one cannot have superior science and inferior morals. The combination is unstable and self-destroying.
It has yet to be proven that intelligence has any survival value.
The best measure of a man's honesty isn't his income tax return. It's the zero adjust on his bathroom scale.
It was the mark of a barbarian to destroy something one could not understand.
My favorite definition of an intellectual: 'Someone who has been educated beyond his/her intelligence'.
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
Before the discovery of quantum mechanics, the framework of physics was this: If you tell me how things are now, I can then use the laws of physics to calculate, and hence predict, how things will be later.
Medicine is a social science, and politics is nothing else but medicine on a large scale. Medicine, as a social science, as the science of human beings, has the obligation to point out problems and to attempt their theoretical solution: the politician, the practical anthropologist, must find the means for their actual solution. The physicians are the natural attorneys of the poor, and social problems fall to a large extent within their jurisdiction.
It's not going to be just humans colonizing space, it's going to be life moving out from the Earth, moving it into its kingdom. And the kingdom of life, of course, is going to be the universe.
Challenges in medicine are moving from 'Treat the symptoms after the house is on fire' to 'Can we preserve the house intact?'
Geography is just physics slowed down, with a couple of trees stuck in it.
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