Science is a broad term describing a number of fields of study or knowledge. While it can be colloquially used to refer to a number of skills, its usage in this wiki generally refers to the system of discovery and invention based on empirical evidence and experimentation rooted in methodological naturalism. The means by which science is executed is known as the scientific method.
The primary anti-science claim of apologists is that science cannot provide sufficiently accurate knowledge about reality as it relies on naturalistic methodologies which exclude supernatural explanations.
Another common anti-science claim is that since there are so many things that science doesn't have the answers for, it is incomplete and thus unworthy of belief.
Many people dismiss the findings of science because science "keeps changing", because that supposedly makes it unreliable.
Science has proven to be the only consistently reliable method of defining reality. Science, by definition, cannot consider supernatural explanations as they are simply unverifiable assertions. Supernatural explanations have yet to provide any reliable, verifiable information about reality, and hence remain a matter of faith. If a supernatural claim does contain scientifically testable assertions, then those assertions may be tested to see if they hold up in nature. However, even if the tests verify the assertions, the supernatural claim itself will remain unverified until the remaining parts of it that previously had no way of being tested do.
The fact that science doesn't currently have all the answers to every question about life, the universe, and everything certainly doesn't mean that science as a whole is unreliable. Two centuries ago science had very little information (and in many cases none at all) about things like quantum mechanics, dark matter, the age of the universe, etc. However, nowadays we know much more simply because science is constantly progressing. Indeed, the rate of scientific progression seems to increase the more we learn. It's not illogical to expect that we will soon have answers for those questions that Creationists (for example) tout as holes in scientific knowledge.
By contrast, religion does not appear to advance human knowledge in any consistent or reliable way.