Get categories query not working in function.php

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You are using third party code to generate those meta boxes, and I am not familiar with how that code works. In fact, based on your question I am not even sure exactly where the code fails. Your description of the problem is inadequate. I can point out that your code is overly complex. It can be simplified considerably:

function get_destinations(){
  // Using a post type
  $args = array(
    'type'                     => 'book',
    'taxonomy'                 => 'genre',
  ); 
  $categories = get_terms($args); // changed to get_terms()

  if (!is_wp_error()) {
    $destinations = wp_list_pluck($categories,'cat_name');
    /* Convert to key=>value format
       I doubt this is actually necessary and can probably be omitted
    */
    $destinations = array_combine($destinations,$destinations);
    return $destinations;
  }
}
var_dump(get_destinations());
  1. Remove the default arguments. You don’t need to repeat those.
  2. Use get_terms() as it returns a proper WP_Error object instead
    of only a part of one (at least on my install, which I may have
    broken. I do that periodically). At any rate, get_terms() makes
    more since as you are not retrieving “categories” but a custom
    taxonomy.
  3. Verify that you have proper term results before trying to use them
  4. Use wp_list_pluck() to simplify the foreach

As far as Core code, I only see three places where this can fail:

  1. The post type is wrong
  2. The taxonomy is wrong
  3. There are not posts in the type/taxonomy