Pagination comments not working

I’m working on a custom theme and I’m trying to paginate my comments. However the links to the comment pages appear but every page displays all the comments. For example: I have 15 comments and every comment page should display 5. so there are 3 pages but each of them display all 15.

I already tried fixing the setting in discussion but it seems to have no effect. Is there a way my coding could have messed this up?

Here’s the page I’m working on:
https://messiahcollege.ph/wordpress/?p=14&cpage=2#comments

Here’s the comments.php:

<?php

	if (!empty($_SERVER['SCRIPT_FILENAME']) && 'comments.php' == basename($_SERVER['SCRIPT_FILENAME']))
		die ('Please do not load this page directly. Thanks!');

	if ( post_password_required() ) { ?>
		This post is password protected. Enter the password to view comments.
	<?php
		return;
	}
?>

<?php if ( have_comments() ) : ?>

	<h2 id="comments"><?php comments_number('No Responses', 'One Response', '% Responses' );?></h2>

	<div class="navigation">
		<div class="next-posts"><?php previous_comments_link() ?></div>
		<div class="prev-posts"><?php next_comments_link() ?></div>
	</div>

<ol class="commentlist" dir="rtl">

<p><?php foreach ($comments as $comment) : ?></p>
<li>

<cite>

<p2><img src="<?php bloginfo('template_url'); ?>/images/speechbubble.png" class="speechbubble"><span class="author"><?php comment_author_link() ?></span> <font color="#8f8f8f">said on</font> <a href="#comment-<?php comment_ID() ?>" title=""><?php comment_date('F jS, Y') ?></a> <?php edit_comment_link('edit','??',''); ?>
</p2>
</cite>

<p><div class="commenttext" dir="ltr">
<?php if(function_exists('get_avatar')) { ?>
<span class="authorlink">
<?php echo get_avatar($comment, '50'); ?>
</span>
<?php } ?>
<?php comment_text() ?></div>
<?php if ($comment->comment_approved == '0') : ?>
<em>Your comment is awaiting moderation.</em>
<?php endif; ?>
</p>
</li>

<?php
/* Changes every other comment to a different class */
$oddcomment = ( empty( $oddcomment ) ) ? 'class="alt" ' : '';
?>
<?php endforeach; /* end for each comment */ ?>
</ol>

	<div class="navigation">

    <?php
    //Create pagination links for the comments on the current post.
    paginate_comments_links();
    ?>

	</div>

 <?php else : // this is displayed if there are no comments so far ?>

	<?php if ( comments_open() ) : ?>
		<!-- If comments are open, but there are no comments. -->

	 <?php else : // comments are closed ?>

	<?php endif; ?>

<?php endif; ?>

<?php if ( comments_open() ) : ?>

<div id="respond">

	<h2><?php comment_form_title( 'Leave a Comment', 'Leave a Comment to %s' ); ?></h2>

	<div class="cancel-comment-reply">
		<?php cancel_comment_reply_link(); ?>
	</div>

	<?php if ( get_option('comment_registration') && !is_user_logged_in() ) : ?>
		<p>You must be <a href="<?php echo wp_login_url( get_permalink() ); ?>">logged in</a> to post a comment.</p>
	<?php else : ?>

	<form action="<?php echo get_option('siteurl'); ?>/wp-comments-post.php" method="post" id="commentform">

		<?php if ( is_user_logged_in() ) : ?>

			<span id="loggedin">Logged in as <br /> <a href="<?php echo get_option('siteurl'); ?>/wp-admin/profile.php"><?php echo $user_identity; ?></a> <br /><a id="logoutb" href="<?php echo wp_logout_url(get_permalink()); ?>" title="Log out of this account">Log out?</a></span>

		<?php else : ?>

			<div id="author">

				<input type="text" name="author" id="authorbox" value="<?php echo esc_attr($comment_author); ?>" size="22" tabindex="1" <?php if ($req) echo "aria-required='true'"; ?> />
				<label for="author">Your Name <?php if ($req) echo "*"; ?></label>
			</div>

			<div id="email">
				<input type="text" name="email" id="emailbox" value="<?php echo esc_attr($comment_author_email); ?>" size="22" tabindex="2" <?php if ($req) echo "aria-required='true'"; ?> />
				<label for="email">Your Email <?php if ($req) echo "*"; ?><br /><font size="2">(will not be published)</font></label>
			</div>

			<div id="url">
				<input type="text" name="url" id="urlbox" value="<?php echo esc_attr($comment_author_url); ?>" size="22" tabindex="3" />
				<label for="url">Your Website</label>
			</div>

		<div id="logout"><?php wp_loginout(); ?>?</div>	

		<div id="required">
		*required
		</div>

		<?php endif; ?>

		<!--<p>You can use these tags: <code><?php echo allowed_tags(); ?></code></p>-->

		<div>
			<textarea name="comment" id="comment" cols="58" rows="10" tabindex="4"></textarea>
		</div>

		<div>
			<input name="submit" type="submit" id="submit" tabindex="5" value="Submit Comment" />
			<?php comment_id_fields(); ?>
		</div>

		<?php do_action('comment_form', $post->ID); ?>

	</form>

	<?php endif; // If registration required and not logged in ?>

</div>
</div>

<?php endif; ?>