Assuming you talk about a "compiler" that uses C as a backend language (like the early C++ compilers did), then there are several good reasons for this:
- C compilers are available for any platform -> your language is available on any platform and architecture where C is available
- C compilers can agressively optimize -> you do not have to care any register allocation, common sub-expression elimination, loop unrolling, etc.
- C language is easier to understand than any "proprietary" intermediate language
The cons are the additional compilation step for the C compiler. But that is easily balanced for a student project by the above mentioned benefits.
Cheers
Andi