Java does support a form of multiple inheritance; a class can implement more than one interface. But in Java you can't extend multiple classes.
You never really need this in real applications, and it leads to problems like the diamond problem. In C++ this is solved by making things more complicated - you can choose between virtual inheritance and non-virtual inheritance in C++.
One of the goals that the designers of the Java language had was to make it simpler than C++, so they decided to not support multiple inheritance in Java.