Unable to create a new taxonomy

Use the conditional tag post_type_exists() to check if the post type book exists, if it exists add taxonomy to it otherwise not

<?php

if( post_type_exists( 'book' ){
add_action( 'init', 'create_book_taxonomies' );

// create two taxonomies, genres and writers for the post type "book"
function create_book_taxonomies() {
    // Add new taxonomy, make it hierarchical (like categories)
    $labels = array(
        'name'              => _x( 'Genres', 'taxonomy general name', 'textdomain' ),
        'singular_name'     => _x( 'Genre', 'taxonomy singular name', 'textdomain' ),
        'search_items'      => __( 'Search Genres', 'textdomain' ),
        'all_items'         => __( 'All Genres', 'textdomain' ),
        'parent_item'       => __( 'Parent Genre', 'textdomain' ),
        'parent_item_colon' => __( 'Parent Genre:', 'textdomain' ),
        'edit_item'         => __( 'Edit Genre', 'textdomain' ),
        'update_item'       => __( 'Update Genre', 'textdomain' ),
        'add_new_item'      => __( 'Add New Genre', 'textdomain' ),
        'new_item_name'     => __( 'New Genre Name', 'textdomain' ),
        'menu_name'         => __( 'Genre', 'textdomain' ),
    );

    $args = array(
        'hierarchical'      => true,
        'labels'            => $labels,
        'show_ui'           => true,
        'show_admin_column' => true,
        'query_var'         => true,
        'rewrite'           => array( 'slug' => 'genre' ),
    );

    register_taxonomy( 'genre', array( 'book' ), $args );

    // Add new taxonomy, NOT hierarchical (like tags)
    $labels = array(
        'name'                       => _x( 'Writers', 'taxonomy general name', 'textdomain' ),
        'singular_name'              => _x( 'Writer', 'taxonomy singular name', 'textdomain' ),
        'search_items'               => __( 'Search Writers', 'textdomain' ),
        'popular_items'              => __( 'Popular Writers', 'textdomain' ),
        'all_items'                  => __( 'All Writers', 'textdomain' ),
        'parent_item'                => null,
        'parent_item_colon'          => null,
        'edit_item'                  => __( 'Edit Writer', 'textdomain' ),
        'update_item'                => __( 'Update Writer', 'textdomain' ),
        'add_new_item'               => __( 'Add New Writer', 'textdomain' ),
        'new_item_name'              => __( 'New Writer Name', 'textdomain' ),
        'separate_items_with_commas' => __( 'Separate writers with commas', 'textdomain' ),
        'add_or_remove_items'        => __( 'Add or remove writers', 'textdomain' ),
        'choose_from_most_used'      => __( 'Choose from the most used writers', 'textdomain' ),
        'not_found'                  => __( 'No writers found.', 'textdomain' ),
        'menu_name'                  => __( 'Writers', 'textdomain' ),
    );

    $args = array(
        'hierarchical'          => false,
        'labels'                => $labels,
        'show_ui'               => true,
        'show_admin_column'     => true,
        'update_count_callback' => '_update_post_term_count',
        'query_var'             => true,
        'rewrite'               => array( 'slug' => 'writer' ),
    );

    register_taxonomy( 'writer', 'book', $args );
}

}

Or if you haven’t created post type book yet, you can do so as:

/**
 * Register a custom post type called "book".
 *
 * @see get_post_type_labels() for label keys.
 */
function wpdocs_codex_book_init() {
    $labels = array(
        'name'                  => _x( 'Books', 'Post type general name', 'textdomain' ),
        'singular_name'         => _x( 'Book', 'Post type singular name', 'textdomain' ),
        'menu_name'             => _x( 'Books', 'Admin Menu text', 'textdomain' ),
        'name_admin_bar'        => _x( 'Book', 'Add New on Toolbar', 'textdomain' ),
        'add_new'               => __( 'Add New', 'textdomain' ),
        'add_new_item'          => __( 'Add New Book', 'textdomain' ),
        'new_item'              => __( 'New Book', 'textdomain' ),
        'edit_item'             => __( 'Edit Book', 'textdomain' ),
        'view_item'             => __( 'View Book', 'textdomain' ),
        'all_items'             => __( 'All Books', 'textdomain' ),
        'search_items'          => __( 'Search Books', 'textdomain' ),
        'parent_item_colon'     => __( 'Parent Books:', 'textdomain' ),
        'not_found'             => __( 'No books found.', 'textdomain' ),
        'not_found_in_trash'    => __( 'No books found in Trash.', 'textdomain' ),
        'featured_image'        => _x( 'Book Cover Image', 'Overrides the “Featured Image” phrase for this post type. Added in 4.3', 'textdomain' ),
        'set_featured_image'    => _x( 'Set cover image', 'Overrides the “Set featured image” phrase for this post type. Added in 4.3', 'textdomain' ),
        'remove_featured_image' => _x( 'Remove cover image', 'Overrides the “Remove featured image” phrase for this post type. Added in 4.3', 'textdomain' ),
        'use_featured_image'    => _x( 'Use as cover image', 'Overrides the “Use as featured image” phrase for this post type. Added in 4.3', 'textdomain' ),
        'archives'              => _x( 'Book archives', 'The post type archive label used in nav menus. Default “Post Archives”. Added in 4.4', 'textdomain' ),
        'insert_into_item'      => _x( 'Insert into book', 'Overrides the “Insert into post”/”Insert into page” phrase (used when inserting media into a post). Added in 4.4', 'textdomain' ),
        'uploaded_to_this_item' => _x( 'Uploaded to this book', 'Overrides the “Uploaded to this post”/”Uploaded to this page” phrase (used when viewing media attached to a post). Added in 4.4', 'textdomain' ),
        'filter_items_list'     => _x( 'Filter books list', 'Screen reader text for the filter links heading on the post type listing screen. Default “Filter posts list”/”Filter pages list”. Added in 4.4', 'textdomain' ),
        'items_list_navigation' => _x( 'Books list navigation', 'Screen reader text for the pagination heading on the post type listing screen. Default “Posts list navigation”/”Pages list navigation”. Added in 4.4', 'textdomain' ),
        'items_list'            => _x( 'Books list', 'Screen reader text for the items list heading on the post type listing screen. Default “Posts list”/”Pages list”. Added in 4.4', 'textdomain' ),
    );

    $args = array(
        'labels'             => $labels,
        'public'             => true,
        'publicly_queryable' => true,
        'show_ui'            => true,
        'show_in_menu'       => true,
        'query_var'          => true,
        'rewrite'            => array( 'slug' => 'book' ),
        'capability_type'    => 'post',
        'has_archive'        => true,
        'hierarchical'       => false,
        'menu_position'      => null,
        'supports'           => array( 'title', 'editor', 'author', 'thumbnail', 'excerpt', 'comments' ),
    );

    register_post_type( 'book', $args );
}

add_action( 'init', 'wpdocs_codex_book_init' );

add_action( 'init', 'create_book_taxonomies' );

// create two taxonomies, genres and writers for the post type "book"
function create_book_taxonomies() {
    // Add new taxonomy, make it hierarchical (like categories)
    $labels = array(
        'name'              => _x( 'Genres', 'taxonomy general name', 'textdomain' ),
        'singular_name'     => _x( 'Genre', 'taxonomy singular name', 'textdomain' ),
        'search_items'      => __( 'Search Genres', 'textdomain' ),
        'all_items'         => __( 'All Genres', 'textdomain' ),
        'parent_item'       => __( 'Parent Genre', 'textdomain' ),
        'parent_item_colon' => __( 'Parent Genre:', 'textdomain' ),
        'edit_item'         => __( 'Edit Genre', 'textdomain' ),
        'update_item'       => __( 'Update Genre', 'textdomain' ),
        'add_new_item'      => __( 'Add New Genre', 'textdomain' ),
        'new_item_name'     => __( 'New Genre Name', 'textdomain' ),
        'menu_name'         => __( 'Genre', 'textdomain' ),
    );

    $args = array(
        'hierarchical'      => true,
        'labels'            => $labels,
        'show_ui'           => true,
        'show_admin_column' => true,
        'query_var'         => true,
        'rewrite'           => array( 'slug' => 'genre' ),
    );

    register_taxonomy( 'genre', array( 'book' ), $args );

    // Add new taxonomy, NOT hierarchical (like tags)
    $labels = array(
        'name'                       => _x( 'Writers', 'taxonomy general name', 'textdomain' ),
        'singular_name'              => _x( 'Writer', 'taxonomy singular name', 'textdomain' ),
        'search_items'               => __( 'Search Writers', 'textdomain' ),
        'popular_items'              => __( 'Popular Writers', 'textdomain' ),
        'all_items'                  => __( 'All Writers', 'textdomain' ),
        'parent_item'                => null,
        'parent_item_colon'          => null,
        'edit_item'                  => __( 'Edit Writer', 'textdomain' ),
        'update_item'                => __( 'Update Writer', 'textdomain' ),
        'add_new_item'               => __( 'Add New Writer', 'textdomain' ),
        'new_item_name'              => __( 'New Writer Name', 'textdomain' ),
        'separate_items_with_commas' => __( 'Separate writers with commas', 'textdomain' ),
        'add_or_remove_items'        => __( 'Add or remove writers', 'textdomain' ),
        'choose_from_most_used'      => __( 'Choose from the most used writers', 'textdomain' ),
        'not_found'                  => __( 'No writers found.', 'textdomain' ),
        'menu_name'                  => __( 'Writers', 'textdomain' ),
    );

    $args = array(
        'hierarchical'          => false,
        'labels'                => $labels,
        'show_ui'               => true,
        'show_admin_column'     => true,
        'update_count_callback' => '_update_post_term_count',
        'query_var'             => true,
        'rewrite'               => array( 'slug' => 'writer' ),
    );
 register_taxonomy( 'writer', 'book', $args );

// Following code will assign default taxonomy to genre taxonomy
    if( !term_exists( 'intelligence', 'genre' ) ){
    $parent_term = term_exists( 'genre', 'genre' ); 
     wp_insert_term(
       'Intelligence',
       'genre',
        array(
           'description'=> 'Book about Intelligence',
           'slug' => 'intelligence',
           'parent'=> $parent_term['term_id']
        )
    );
  }
}

I have tested this code and it works, it should work for you as well

If you want to add your custom taxonomies to wordpress post then use:

register_taxonomy( 'writer', array( 'book', 'post' ), $args );