Override private status – Enable users to read private posts

As already mentioned in the comments, private posts are private for a good reason.

If you want to change this behaviour, you could probably alter the get_posts() which is used to retrieve your posts.

I did not try it, but this could work:

$args = array(
    'post_status' => array(
                         'publish',
                         'private'
                     )
);
$myposts = get_posts($args);