You have literally hundreds of systems working in concert and tied to more hundreds of physical components coming under extreme temperature and pressure conditions, some of which can interact in the weirdest and most unexpected ways - certainly not ones you'd always think to model. The chances that any one of those does something unexpected is not low, and the chances that it cascades into a much larger failure is non-significant.
edit: It's also sometimes a human problem - thousands of people working on this together, and all sorts of different incentives. Here's a famous example of a failure, and the PR kerfuffle that ensued: https://en.wikipedia.org/wiki/Rogers_Commission_Report
Quoth Feynman:
"It appears that there are enormous differences of opinion as to the probability of a failure with loss of vehicle and of human life. The estimates range from roughly 1 in 100 to 1 in 100,000. The higher figures come from the working engineers, and the very low figures from management. What are the causes and consequences of this lack of agreement? Since 1 part in 100,000 would imply that one could put a Shuttle up each day for 300 years expecting to lose only one, we could properly ask "What is the cause of management's fantastic faith in the machinery? .. It would appear that, for whatever purpose, be it for internal or external consumption, the management of NASA exaggerates the reliability of its product, to the point of fantasy."