I use the 12 hour clock because that's what everyone else uses. When you tell a woman you will pick her up for a date at "1900 hours", it will weird her out, and you don't want to weird a woman out, especially on a first date. But the 24 hour clock is superior, and has several advantages.
It's less confusing; Think about setting the alarm on your phone. How many times have you set the hour and the minute, but forgot to do the AM/PM part because you assumed it was set to AM?
It is a bit more useful for computer programming tasks, which granted, does not affect a lot of people.
Who ever thought up the 12 hour concept didn't think it all the way through. Why would you have the same designation for two totally different times every day? Sure, you can go through the extra step of designating AM or PM, but that's not very mathematically elegant.