Why Can't Programmers.. Program?

Anecdotal “evidence” against this: When I started my first job after university (also, my first programming job), I could /maybe/ have answered FizzBuzz in Java. I’d programmed probably less than 1000 lines my whole life. Two months later I was improving my colleagues’ code in a language I’d never used before. 2.5 years, some 36,000 lines of production code, and a good recommendation letter later, I’m stuck in a job market that only wants people with 5 years experience.