When Stroustroup created C++ it was a superset of C. In fact, the earliest compilers for C++ were a pre-processing pass that generated C code to be compiled by (then) K&R and soon ANSI C compilers. Since then C++ has grown massively and has specialized compilers that optimize the many new constructs. Many C++ programmers only use a subset of the current language. A common team situation is that every team member uses a different subset of C++.
IMO since C is the ancestor of C++ as well as ObjectiveC/Swift, C#, JavaScript, Java by learning pure C, you gain the foundations from which to learn not just C++ but those other languages.
Other languages can be transpiled to C (f2c from 1990 for Fortran, p2c from 1989 for Pascal) so cfront's C++->C conversion isn't really connected to the idea of superset-ness.
I've heard the argument that learning Latin first makes it easier to learn the Romance languages which derive from it. I don't believe it, in part because I found what helps me most to learn a language is actually having a need to use it (like visiting Germany for the first time after a year of German classes at school.) Start by learning the language you're going to use. Don't start with Algol simply because it's the historic foundation to C, Pascal, PL/1, etc.
Someone starting with K&R as a way to learn C++ will need to discard some styles, like using malloc/free. (And someone starting with Latin as a way to learn Spanish means discarding most of Latin's case system.)
IMO since C is the ancestor of C++ as well as ObjectiveC/Swift, C#, JavaScript, Java by learning pure C, you gain the foundations from which to learn not just C++ but those other languages.