I want to display my custom post type arranged by taxonomy

That’s because you’re echoing the Parent term name outside of the loop.

$custom_terms = get_terms('material_category');

foreach($custom_terms as $custom_term) {
    $args = array('post_type' => 'materials',
        'tax_query' => array(
            array(
                'taxonomy' => 'material_category',
                'field' => 'slug',
                'terms' => array('general-english')
            ),
        ),
    );

    $loop = new WP_Query($args);
    if ($loop->have_posts()) {
        while ($loop->have_posts()) : $loop->the_post();
            echo '<h2>' . $custom_term->name . '</h2>';
            echo '<a href="' . get_permalink() . '">' . get_the_title() . '</a>';
        endwhile;
    }
    wp_reset_query();
}