1st Place in Derby #332: Evolution, with 202 votes!
Paleontology is an interesting branch of science. Unlike other sciences that can conduct experiments and test hypotheses directly, paleontology must rely on inductive reasoning to reach probabilistic conclusions about the past.
What the hell does that mean? Take the example of Archaeopteryx, one of the best-known and most important fossil specimens in the history of paleontology. Archaeopteryx is considered a "missing link" between dinosaurs and birds because it shares many characteristics specific to each group, but it's impossible to tell whether it was DEFINITELY a missing link. The best we can do is make a series of very well-informed conclusions based on available data.
For instance, the Archaeopteryx skeleton lacks certain features of modern birds such as a fused breastbone and toothless beak, but DOES have many features of modern birds capable of powered flight. Most importantly, the fossil of Archaeopteryx is so detailed that it's possible to tell that it had asymmetrical feathers.
Why are asymmetrical feathers important? Well, it turns out that modern birds that fly have asymmetrical feathers that are short and fat at the leading edge and long and tapered in the read (like a modern airplane wing), whereas modern flightless birds have symmetrical feathers.
So it seems clear, right? Modern birds with flight have asymmetrical feathers and Archaeopteryx had asymmetrical feathers so it was capable of flight. But, and this is where paleontology is weird: A rogue professor could always argue that Archaeopteryx was just weird and happened to have asymmetrical feathers but was NOT capable of flight. Maybe it was attractive to the opposite sex to have asymmetrical feathers, or maybe it kept parasites out -- who knows!
This professor wouldn't be wrong because there's no way to prove that he's wrong, but it is possible to say that he's very probably wrong, given the available evidence. And that's what makes historical sciences like paleontology so goofy -- it's about building probabilistic arguments rather than deducing undeniable truths.