The class definition gives you an audit trail, so you can see from looking at the class which functions have permission to modify the private parts of the class. If a function is a friend, it means that it isn’t a member, but you want to give permission to modify private data anyway, and it must be listed in the class definition so everyone can see that it’s one of the privileged functions.

C++ is a hybrid object-oriented language, not a pure one, and friend was added to get around practical problems that crop up. It’s fine to point out that this makes the language less “pure,” because C++ is designed to be pragmatic, not to aspire to an abstract ideal.