Why operator overloading functions can't be members of class

[rawfool]

For example, overloading operator<<

#include <iostream>
#include <string>
#include <vector>
#include <boost/algorithm/string.hpp>
 
using namespace std;
 
class String
{
    string d_name;
public:
    String(string const & s) : d_name(s) {}
    vector<String> split(string const & delimiter = " ") const
    {
        vector<string> parts;
        boost::split(parts, d_name, boost::is_any_of(delimiter), boost::token_compress_on);
        return vector<String>(parts.begin(), parts.end());
    }
    friend ostream & operator<<(ostream & out, String & obj);    // making it as friend function for the convinience of accessing private data members
};
 
ostream & operator<<(ostream & out, String & obj)
{
    return out << obj.d_name << endl;     // If not a friend, obj.getName(): string const & getName() const { return d_string; }
}
 
int main()
{
    String s{"This is a test string"};
    vector<String> v = s.split();
 
    vector<String>::iterator it;
    for(it = v.begin(); it != v.end(); ++it)
        cout << *it << endl;
}

#include <iostream>
#include <string>
#include <vector>
#include <boost/algorithm/string.hpp>

using namespace std;

class String
{
    string d_name;
public:
    String(string const & s) : d_name(s) {}
    vector<String> split(string const & delimiter = " ") const
    {
        vector<string> parts;
        boost::split(parts, d_name, boost::is_any_of(delimiter), boost::token_compress_on);
        return vector<String>(parts.begin(), parts.end());
    }
    friend ostream & operator<<(ostream & out, String & obj);    // making it as friend function for the convinience of accessing private data members
};

ostream & operator<<(ostream & out, String & obj)
{
    return out << obj.d_name << endl;     // If not a friend, obj.getName(): string const & getName() const { return d_string; }
}

int main()
{
    String s{"This is a test string"};
    vector<String> v = s.split();
    
    vector<String>::iterator it;
    for(it = v.begin(); it != v.end(); ++it)
        cout << *it << endl;
}

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Why is the ostream & operator<<(ostream & out, String & obj) cannot be a member function?
I mean, I don't understand the rule that - "operators << and >>, whose left operands are stream classes from the standard library which you cannot change". Kindly help me understand this.
Thanks.