Because implementing an interface is not inheritance. It simply means that your class will adhere to a predefined contract, typically to provide a set of methods related to a certain functionality. Any class can adhere to many such contracts without conflict (unless two of those interfaces define the same method).
Unlike inheritance, it does not automagically receive attributes or functionality due to a hierarchical relationship with its superclass since no such relationship exists.
Multiple inheritance is basically not allowed in Java or many other OO languages due to the already mentioned Diamond Inheritance problem.
