Here's what evolution-deniers don't seem to understand

This Raw Story article perfectly crystallizes what's wrong with those who attack the Theory of Evolution:

1. It’s just a theory
[...] Although people use “theory” in everyday conversation to mean a not necessarily proven hypothesis, this is not the case in scientific terms. A scientific theory typically means a well substantiated explanation of some aspect of the natural world that sits above laws, inferences, and tested hypotheses. 

2. Humans are descended from monkeys
No, your great-great-great-ancestor was not a monkey. Evolution theory indicates that we have common ancestors with monkeys and apes – among the existing species, they are our closest relatives. Humans and chimpanzees share more than 90% of their genetic sequence. But this common ancestor, which roamed the earth approximately 7m years ago was neither a monkey nor a human, but an ape-like creature that recent research suggests had traits that favoured the use of tools. 

3. Natural selection is purposeful
There are many organisms that are not perfectly adapted to their environment. [...] Natural selection can only randomly favour the best of what is available, it does not purposefully turn all living organisms into one super creature.
[...] Still, selection of the best option possible has led to an amazing diversity of forms remarkably well adapted to their environments, even if not perfect. 

4. Evolution can’t explain complex organs
A common argument in favour of creationism is the evolution of the eye. A half developed eye would serve no function, so how can natural selection slowly create a functional eye in a step-wise manner? Darwin himself suggested that the eye could have had its origins in organs with different functions. Organs that allow detection of light could then have been favoured by natural selection, even if it did not provide full vision. These ideas have been proven correct many years later by researchers studying primitive light-sensing organs in animals. In molluscs like snails and segmented worms, light-sense cells spread across the body surface can tell the difference between light and dark. 

5. Religion is incompatible with evolution
It is important to make it clear that evolution is not a theory about the origin of life. It is a theory to explain how species change over time.

There is more at the source, but you get the gist.

Evolution is not disputable. It is a scientifically established fact.