Michael,
Your website and your Facebook Page are different places altogether. When a user places a comment on a Joomla article, it will not automatically show up on your Facebook Page. That's how Facebook works as comments on an article have relevance to that article. If they are just posted directly on your Facebook Page, the content that is being commented on won't be shown and the comment itself may not make sense.
I hope that helps explain, but if you need more assistance or have a specific example of something you think should be happening, just let me know.
Thanks,
Alex