Below is a condensed version that chapter of his book. The reason is simple. If we know that suffering is inherent in life, then when suffering visits us, we wouldn't be too surprised. Of course we will try to alleviate or overcome it, but when that is not possible, such as when we are having an incurable disease, we can accept and learn to live with it. On the other hand, the person who refuses to acknowledge the fact of sufferings, suffer all the more when he finds difficulty in reconciling with his suffering.
Mindfulness is the key.
It can help us to live remarkably well with pain. A meditator, for instance, can observe painful sensations during his sitting meditation. He can feel it. He can observe its intensity. He can see its changes, how like the music in an orchestra, it increases to a deafening cresendo, or how it rises and falls as if in waves.