There's a surprising amount of perfectly valid C code that's not valid C++ (not even taking regrettable design warts like VLAs into account). The "common subset" of C and C++ is both a subset of C, and a subset of C++, e.g. C++ has forked C and turned its C subset into a non-standard dialect.

It's interesting that the other C descendant Objective-C has decided to "respect" its C subset instead of messing with it, with the result that new C standards are automatically supported in ObjC.