why don't c++ compilers interpretation operator== operator!=?

i am large fan permitting compiler many work possible. minute rudimentary category compiler give following 'free':

• a default (empty) constructor


• a duplicate constructor


• a destructor


• an assignment user (operator=)

but can't seem give any comparison operators - such operator== operator!=. example:

class foo
{
public:
    std::string str_;
    int n_;
};

foo f1;        // works
foo f2(f1);    // works
foo f3;
f3 = f2;       // works

if (f3 == f2)  // fails
{ }

if (f3 != f2)  // fails
{ }

is there good reason this? since behaving member-by-member comparison problem? apparently category allocates memory following you'd wish careful, nonetheless rudimentary category definitely compiler you?