In a nutshell - His reasoning was that he didn't feel like he was in love with either one of them, and didn't want to give them false hope by proposing. He felt it was the honorable thing to do to say bye to both of them, rather than choosing one and ending it later.
I watched the "After the Final Rose" show the day after the finale. Poor Deanna thought that Brad would change his mind and get back with her.
This is the first season of the Bachelor that I watched. I felt gypped at the end when he didn't choose anyone!
I bet you could watch the finale on abc.com.