Xcode 5 is behaving just fine, and I\'m able to build and run apps on my iOS 7 device and in the iOS 7 simulator.
However, I do want to support iOS 6.1, but I don\'t
All you have to do is go to Xcode -> Preferences -> Choose the "Downloads" tab and install the iOS 6.0 Simulator.
Once you're done downloading it, it should show up as an option in your schemes.