Problem with 'register_activation_hook' using static function

Hello

I’m now building a plugin using class and facing a problem.
I created a class as below, which is a simplified version,

class MyClass
{
 public static function register_activation_hook()
 {
  $new_page = array(
   'comment_status' => 'closed',
   'ping_status'    => 'closed',
   'post_content'   => 'default content',
   'post_status'    => 'publish',
   'post_title'     => 'default title',
   'post_type'      => 'page'
  );
  $new_page_id = wp_insert_post( $new_page );
 }

 public function __construct()
 {
  //
 }
}

register_activation_hook( __FILE__, MyClass::register_activation_hook );
$myClass = new MyClass();

If I activate it, it returns an error message,

Fatal error: Call to a member function get_page_permastruct() on a non-object in /homepages/mysite/wp-includes/link-template.php on line 271

It seems that $new_page_id = wp_insert_post( $new_page ); causes the error.

If I make register_activation_hook as just public function and call it within the constructor, it works fine. I don’t think that it doesn’t really matter but I would like to know why it doesn’t work…
Any tip or help would be grateful!

Many thanks