Typically someone who doesn't believe in evolution believes that everything was created as it is now ~6000 years ago. The small-scale genetic changes that certain species experience over time, they claim, is not evolution. Usually the sticking point is the age of the earth, because if the earth really IS ~5 billion years old, then there is plenty of time for these small scale changes to snowball into differentiated species. You're usually better off debating the age of the Earth, because that is their main "fact" that holds up their disbelief of evolution. Of course, there are other avenues of argument, but this is a lot of times the sticking point.