In most cases it is much harder to actually prove something through experiment, whereas it may be comparatively easy to disprove its opposite. In this case "Paper will always be incombustible in air" is actually fairly hard to prove (I recognize this isn't your exact hypothesis, but your hypothesis as stated is not the sort that would lead to theories that could predict things and thus be useful). You would have to prove that in every possible set of conditions (and there are infinitely many) paper burns. This is not feasible. Instead you form an opposite hypothesis, e.g. "paper is not ever combustible in air," and then set out to disprove it. This alternate hypothesis is known as the "null hypothesis." Experimentation is a form of inductive reasoning, not deductive reasoning. As such it takes infinitely many examples to prove something, but only one counterexample to disprove something. By burning the paper, you have disproved your null hypothesis and provided evidence toward your theory.
Thank you, XKCD, for forcing me to look up "null hypothesis" last week.