Showing home button in a specified menu

show_home isn’t working for you because there is no show_home argument on wp_nav_menu. You will need to add it using the menu editor in the admin panel, most likely as a custom link.

These are the valid arguments:

$defaults = array(
    'theme_location'  => '',
    'menu'            => '',
    'container'       => 'div',
    'container_class' => '',
    'container_id'    => '',
    'menu_class'      => 'menu',
    'menu_id'         => '',
    'echo'            => true,
    'fallback_cb'     => 'wp_page_menu',
    'before'          => '',
    'after'           => '',
    'link_before'     => '',
    'link_after'      => '',
    'items_wrap'      => '<ul id="%1$s" class="%2$s">%3$s</ul>',
    'depth'           => 0,
    'walker'          => ''
);

wp_nav_menu( $defaults );

You’ve likely been given an example that has confused wp_nav_menu with wp_page_menu, which does have a show_home argument