Fast Lifting is not more dangerous than slow lifting.
Conventional wisdom states that fast lifting is dangerous and that weights should be moved at a slow, controlled, deliberate pace. The authors maintain, however, that some exercises should be done at that slow pace, and some should be done fast. There are some exercises where it is unnatural to move at a slow deliberate pace, and doing so can deform you muscle and lead to injury more easily than doing the same lift at a naturally quick pace.
In my own experience, my weight lifting tends to be at the slower pace. I tend to save the fast exercises for when I am running or on a bike. I can not necessarily disagree with their points, however. The trick is doing a lift that you are prepared for at a pace conducive to your goals. Even the authors suggest that beginners start with exercises that can be done at a slow, smooth and controlled pace, and that intermediate and advanced lifters need to work up to faster lifts that they have never done before.