People like to throw the word "falsifiability" around as a way to explain how evolution is better than intelligent design, but too many of them don't understand all the implications. The word was invented by Karl Popper to help distinguish science from pseudo science, and what respectability it has is derived from his arguments. So if you are going to rely on falsifiability as a criterion, you have to use it in Popper's sense. The alternative is to spend years writing books to argue that some new meaning of the word is also useful as a criterion.
Popper used Marxism and Freudian psychology as two examples of pseudo science (he had a third example but I don't recall what it was). What he observed about these two schools is that they claimed that their theories could explain things, but there was almost no possible outcome that they could not have explained in some way: this man is obsessive because he was potty trained too early as a child. This other man is obsessive because he was potty trained too late and he is over compensating for the feelings of insecurity from that. Marxism has very similar explanations for economic conditions, but in neither theory is it possible to take a set of conditions and predict a specific outcome. All reasoning is post hoc
--they first look at the entire case with the outcome and then explain the outcome based on the conditions.
I think most people would agree that there is something wrong with a "scientific" theory that works like Freudian analysis or Marxism, but people who study these things (as opposed to armchair philosophers of science) generally agree that Popper's theory of science failed. Two reasons come to mind. First, in contradiction of Popper, science doesn't typically abandon a theory just because it has been falsified. It's much more common to look for extensions to the theory that explain the new data. A contradiction is sometimes around for decades before it is explained, and scientists don't seem to have any trouble with the fact that they are working with a falsified theory.
Second, theories do get confirmed. Regardless of the logical arguments that Popper made, real scientists certainly act like they are working with confirmed theories. Try suggesting that Special Relativity, Quantum Uncertainty, or Evolution is false and see how many scientists tell you "well, we can't really ever confirm a theory but it hasn't been falsified as yet." Far more will respond with hostility at you for not recognizing the obvious truth of the theory.
Third, there are scientific projects that don't make falsifiable theories. Or rather, there is a broad range of scientific endeavors from those where theories are easily and quickly tested to those where testing is practically impossible. In these latter areas such as astronomy, archeology, and paleontology, scientists readily accept other criteria than falsifiability to evaluate theories.
According to Popper the theory must predict basic facts --specifically-observable instances. A theory is not falsifiable just because it can contradict another theory. Since Popper's foundation for science doesn't allow for a theory to be confirmed, only falsified, you get no information when one theory contradicts another that is specific to either theory.
Now let's get to evolution, by which I mean the theory that all life originated and evolved through purely physical events. This theory is much more like Freudian analysis than like physics. It doesn't make any hard, testable predictions, all it does is explain things after the fact. You see this structure in an animal? Well it might have evolved like this. You can't find any evidence that it evolved like that? Well, maybe it evolved in some other way. Who knows? Of course, like Freudian analysis, evolution does give some very neat explanations for certain things like the fact that animals that originated in isolated areas tend to be unable to compete with animals that originated in very large areas, but those are after-the fact explanations. According to the falsification criterion, those don't count. (and by the way, one can accept the existence of natural selection without the broader theory of evolution).
Evolution seems to make some general predictions, but in those cases it has sometimes been wrong. For example it should be possible to find evolutionary tracks in the fossil record that show the evolution of a particular species. Peleontologists don't find these tracks, but they don't think that this failure falsifies evolution, it just shows how sparse the fossil record is. Of course this sparse fossil record stills lets them find certain dinosaurs all over the world in many different digs, but somehow the intermediate stages got lost. Yet although this could count as a falsification, scientists don't acknowledge it as such. If all falsifications are ignore, how falsifiable is the theory?
The purpose of this post is not to argue that the idea of falsifiability is useless --it's not. Falsifiability is a very valuable rule of thumb when applied correctly. But it is not an absolute demarcation of science and it cannot serve as an argument-stopper. When you say that evolution is falsifiable and intelligent design is not, you need to explain exactly how evolution is falsifiable in a way that intelligent design is not, and you need to show that this is relevant and that it does not lead to absurd results.
More on the absurd results later...