September eleventh isn't just the day after September tenth. Unlike August eleventh or April eleventh, it is a day unpleasantly blasted into people's memory.
You may sometimes wonder why we call it 9/11. It isn't as though it is so different from Pearl Harbor or the Ides of March. Here in America we don't normally use dates as a name. We don't, for example say, "I can't wait for December 25th! or, "We don't want another occurrence like December 7th! In fact, the only other date we use as a name is July 4th. However, we also commonly refer to that as Independence Day instead.