In C++, why is private the default visibility for members of classes, but public for structs?
Probably for backwards compatibility with C structs. This way structs declared in C code will continue to work the same way when used in C++ code.
C++ was introduced as a superset of C. Structs were carried over from C, where the semantics of their members was that of public. A whole lot of C code exists, including libraries that were desired to work with C++ as well, that use structs. Classes were introduced in C++, and to conform with the OO philosophy of encapsulation, their members are private by default.
Because a class is the usual way of doing object orientation, which means that member variables should be private and have public accessors - this is good for creating low coupling. Structs, on the other hand, have to be compatible with C structs, which are always public (there is no notion of public and private in C), and don't use accessors / mutators.