It might be true that you don't need to learn the syntax of C if you know the syntax of C++ but you cetainly do need to learn of how coding practices are different in C than in C++.
So your professor wasn't 100% right.
In C you don't have the classes to arrange your code into logical modules and you don't have C++ polymorphism. Yet you still need to achieve these goals somehow.
although the syntax of C is to some extent a subset of C++, programming in C is not a subset of programming in C++. it is completely different.