array_push prevents the page from loading

People please help!
The following code gets all the posts of a specific teacher (teacher is a custom taxonomy) and for each post get the highest category in hierarchy of this post, that is the direct child of a given category. Example: given category is 14. The category hierarchy is: 0->14->32->123, 124, 125 (three categories under 32, each has one post). In this case I get 32 for each post, I push it in the array and then remove identical values. BUT I have a problem in this case: given category is 32. The category hierarchy is the same. In this case I get 123, 124, 125 (direct children of 32). The line that pushes them in the array prevents the page from loading. WHY?!

$categories_to_display = array(); //declare empty array
                        //get all posts of selected teacher
                        $args = array(
                        'post_type' => 'post',
                        'tax_query' => array(
                            array(
                            'taxonomy' => 'teacher',
                            'field' => 'id',
                            'terms' => $teacher_id
                             )
                          )
                        );
                        $query = new WP_Query( $args );
                        
                        // The Loop
                        if ( $query->have_posts() ) {
                            while ( $query->have_posts() ) {
                                $query->the_post();
                                $categories = get_the_category();
                                foreach($categories as $cat)
                                {
                                    $cat_id_to_display = get_nth_parent_category($cat ,$parent_cat_id);
                                    //array_push($categories_to_display, $cat_id_to_display);
                                    $categories_to_display[] = $cat_id_to_display;
                                }
                            }
                        } 
                        /* Restore original Post Data */
                        wp_reset_postdata();
                        $categories_to_display = array_unique($categories_to_display); //remove duplicate values
                        $categories_to_display = array_filter($categories_to_display); //remove false values

The function:

function get_nth_parent_category($cat ,$parent_cat_id_to_stop_at)
{
    $parent_id = $cat->parent;
    if($parent_id == 0)
    {
        if($parent_cat_id_to_stop_at == 0)
        {
            return $cat->term_id;
        }
        else
        {
            return false;
        }
    }
    
    $parent_cat = get_category($parent_id);
   
     if($parent_cat->term_id == $parent_cat_id_to_stop_at)
        {
            return $cat->term_id;
        }
        else
        {
            return get_nth_parent_category($parent_cat, $parent_cat_id_to_stop_at);
        }
}