Off the top of my head I can think of 3 things that would make it difficult to let go with one hand (besides just needing practice)
1. Weak core making you put too much weight on the bars, so you just CAN'T let go. You shouldn't be leaning on the bars. Like Trek said, if you can't ride with just your fingertips touching the bar ("playing piano"), something is wrong.
2. Saddle doesn't fit, so your body has automatically shifted weight onto your hands to protect your hoo-hah. (again, can't "play piano" when you ride, and can't let go with one hand)
3. Bike doesn't fit, cockpit too long so you are lunging out toward the bar and your center of mass is far forward of the cranks, leaving you weightbearing on the arms (can't play piano, etc.)
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson