Why cant I add a custom post type to a custom taxonomy?

The post_category you are using is for core categories taxonomy. For custom taxonomies you have to use tax_input. For example, the next code set terms for custom_tax_category and custom_ta_tag taxonomies.

$args = array(
    'post_type'     => 'custom_post_type',
    'post_title'    => wp_strip_all_tags( $title ),
    'post_content'  => 'some content',
    'post_status'   => 'publish',
    'post_author'   => $author_id,
    'tax_input'     => array(
                           'custom_tax_category' => array( $category_id ),
                           'custom_tax_tag'      => array( $tag_id )
     ),
);
$new_cpt_id = wp_insert_post( $args );