I recently read a book on this subject. (Tried anyway. It was really big). The main argument everyone seems to be making is that computers today aren't like human brains and they aren't fast enough/don't have enough memory. The book argued that technology is advancing exponentially, and in a very short time we would both understand the human brain well enough to model it with a computer and have computers fast enough to manage the model.

Also, DNA and reproduction can easily be managed by a computer. Many technologies are already designed by computer even better than humans could. (Example). Then, if you give the same computer control of a manufacturing plant, not only can it cause evolution, it can control its own evolution. That, I think, is what is ultimately the driving force of the Singularity.

This is the book, by the way