In practice, you never really need multiple inheritance, and it leads to dilemmas like the Diamond problem.
The designers of the Java language decided that multiple inheritance wasn't needed and that it only would make the language unnecessarily complicated, so they left it out. [ May 17, 2007: Message edited by: Jesper Young ]
As Jesper Young said, because the designers of Java thought it made things too complicated. Whoever designs a language has to make such decisions. I found a paper yesterday [Martin P (1998): Java, the good, the bad and the ugly ACM SIGPLAN Notices archive 33: 34 - 39] which says the multiple inheritance model in C++ is poor and Eiffel has a better model.