Forward reference confusion

With reference to the following code, I do not understand why the move constructor is called both with an lvalue and rvalue. I would expect copy ctor to be printed when i pass an lvalue to the push method.

#include <iostream>
#include <string>
#include <vector>
using namespace std;
class my_obj
{
  public:
    my_obj()
    {
        cout << "default ctor\n";
    }
    my_obj(const my_obj& other)
    {
        cout << "copy ctor\n";
    }
    my_obj(my_obj&&  other)
    {
        cout << "move ctor\n";
    }

};
class test
{
    private:
    //my_obj arr[5];// array of my_obj

    public:
    template<typename T>
    void push(T&& object)
    {
         print(forward<T>(object)); // should call the right overload
    }
    template<typename T>
    void print(T&& a) // 
    {
        cout << "move\n";
        my_obj temp = forward<T>(a);
    }
    template<typename T>
    void print(T& a)
    {
        cout << "val\n";
        my_obj temp = forward<T>(a);
    }
};


int main()
{
    my_obj obj;
    test f;

    f.push(obj); // why is move ctor called here? shouldnt it be copy ctor since not rvalue
    cout << "\nPUSHING TEMP\n\n";
    f.push(my_obj {});
}

output:

default ctor
val
move ctor

PUSHING TEMP

default ctor
move
move ctor