Nothing. But if he is going to write C in C++, then what is the point of writing C++? Especially sticking to C gives substantially increased flexibility in terms of language bindings, embedded usage etc.
I've probably spent more years writing C++ code than C code, but I'm all with him on this - if what you need to do for whatever reason don't need/benefit all that much from C++ when accounting for all constraints, then choosing C as being the lowest common denominator between other languages is a very good choice for a library.