When I was learning proof by induction I also initially thought that this was a flaw in inductive reasoning, until I finally learned how to do proof by induction right. You can't give a proof by just showing that the base case and the next case holds. Besides the base case you also need to prove that if n holds, n + 1 also holds, for any n.

So to get a proof by induction that more beer always makes you feel better, you need to objectively prove that if I had n beers another beer (n + 1) will make me feel better. The mistake here is that this student thought that he had an inductive proof after showing he felt better after just two beers (base case + 1).

If only he had done his proof by induction right, he wouldn't need so many experiments. Unless of course the goal of his research was to get as drunk as possible.