You get nothing for your anniversary, graduation, etc. because you can't easily prove these dates. Your birthday is on your driver's license and birth certificate, items most people have. While you could bring in your marriage license or diploma, that's really convoluting the process even more, and Disney would need a 25 page FAQ for the 95% of the population that can't draw inferences. Disney would also be inundated with complaints and questions by the 99% of that 95% that wouldn't read the FAQ, and would just expect Disney to accommodate them. Everyone has a birthday, so by making the freebie available on one's birthday, they effectively reached the entire population (besides those Feb 29 oddballs) without overly complicating the whole promotion.
Even with keeping it simple, as others have pointed out, there will still be a lot of people who don't get it.