First off, Interfaces don't provide multiple inheritance: interfaces are not classes, they are a contract, and you can't "inherit" from an interface.
As to why C# doesn't support MI, the most likely reasons is "because the benefits do not overweigh the complexity involved in implementing it" - and the main reason for that complexity is the Diamond Problem:
Multiple inheritance - Wikipedia[
^]
The diamond problem arises when two classes B and C inherit from A, and another class D also inherits from both B and C. If a method in D calls a method defined in A, and B and C have overridden that method, then which class method should be executed? the version from B, or the version from C?
Although it is possible to get round this (C++ does) it complicates the language and the code you write - and C# is designed to encourage clean, simple, and maintainable code (an accusation not often leveled at C++ code!).