Breadcrumbs not displaying parent or custom post pages

Hi there,
I am relativity new to WordPress & am trying incorporate Breadcrumbs into my own bespoke theme.
In my functions I ave added the following code:

function the_breadcrumb() {
$sep = ' > ';

if (!is_front_page()) {

    echo '<a href="';
    echo get_option('home');
    echo '">';
    bloginfo('name');
    echo '</a>' . $sep;

    if (is_category() || is_single() ){
        the_category(' z ');
    } elseif (is_archive() || is_single()){
        if ( is_day() ) {
            printf( __( '%s', 'text_domain' ), get_the_date() );
        } elseif ( is_month() ) {
            printf( __( '%s', 'text_domain' ), get_the_date( _x( 'F Y', 'monthly archives date format', 'text_domain' ) ) );
        } elseif ( is_year() ) {
            printf( __( '%s', 'text_domain' ), get_the_date( _x( 'Y', 'yearly archives date format', 'text_domain' ) ) );
        } else {
            _e( 'Blog Archives', 'text_domain' );
        }
    }

    if (is_single()) {
        echo $sep;
        the_title();
    }

    if (is_page()) {
        echo the_title();
    }

    if (is_home()){
        global $post;
        $page_for_posts_id = get_option('page_for_posts');
        if ( $page_for_posts_id ) {
            $post = get_page($page_for_posts_id);
            setup_postdata($post);
            the_title();
            rewind_posts();
        }
    }

}
}

Now these breadcrumbs work, but they do NOT display any parent pages or posts at all to let the user know where they are.

Is there a way of doing so within WordPress without the use of a Plugin?

Any help would be really appreciated.

Thank you