September is traditionally the month to start shows. It's the end of summer, school starts up, it makes sense.
May/June is when school gets out and the summer begins, so that is an obvious time for seasons to end.
So you have September to June and a show only produces 21-24 episodes per year. There's your reason.
Many people like the way that Lost and 24 have dealt with their shows, starting in January and going to June, pretty much straight through. The problem is, that leaves a good 6 months of nothing--bad for advertisers, especially in the months leading up to Christmas. It would be like having a 6 month summer, rather than only 3. Execs, advertisers and even a lot of fans of those shows would hate that if it was standard.