Why can't we use base class reference to a derived class object if inheriting privately?

Question

It might be a stupid question, but I'm wondering. If we're inheriting publicly - public methods of base class are becoming public methods of the derived class. If we're inheriting privately - public methods of base class are becoming private methods of derived class. So:

If we're making two classes, like:

Testing1 (which inherits publicly) and Testing2 (which inherits privately):

class Testing1 : public std::string
{
private:
    std::string a;

public:
    Testing1(std::string str = "Null") : a(str) {};
};

class Testing2 : private std::string
{
public:
    Testing2(std::string str = "Null") : std::string(str) {}
};

Why is it that we can make a base class reference in the class where we're inheriting publicly:

Testing1 a;
std::string* ptr1 = &a;
std::string& ref1 = a;

But we can't use the base class reference to a derived class in the class where it's inherited privately?

/* Can't do this */
Testing2 b;
std::string* ptr2 = &b; // -> error
std::string& ref2 = b; // -> error