Interface delegation (as pointed by Leledumbo, and later furter explained by PascalDragon) is much less limited, actually gets you pretty close to real multiple inheritance.
I know everything about interfaces, including interface delegation, and class composition. I actively use them in my project. Problem is - I just feel, that this solution is clunky. I still have to make wrapper classes and some other clunky structures, that implies unnecessary waste of my time and effort. And I just don't like, how my code looks like. I.e. what I want to say, is that multiple inheritance is natural way of describing class structures, I need.
Interface delegation is nothing more, than just virtual multiple inheritance, I've shown above. Virtual multiple inheritance is just more natural. You don't need to look under hood of this process. You don't need to do it manually. Compiler does everything for you.
And at the end everything boils down to quality of code and effectiveness of programming. My project is very large. I don't like both quality of my code and it's performance due to some penalties, caused by extra wrapper classes. I just want to make it better.
Dunno. Just look at my code pattern. Now try to describe it in terms of interface delegation. Do you see any difference?