Redirect to account login or registration

That's likely happening because of the following:
* You are logged into Facebook.com
* You previously authenticated into your site with Facebook
* For some reason, there's no current connection between the Facebook user and any Joomla accounts on your site
* You have "Automatically Log Facebook Users In" enabled.

In that case, JFBConnect is detecting that the user has authenticated with Facebook in the past and tries to log you in. However, there's no account to log that user into, so it's bringing you to the registration page.

To fix, you'll need to either:
1) In Facebook.com, go to Settings -> Apps and delete you're website Application so that JFBConnect won't detect that you've previously authenticated.
2) Actually register (or link to an existing an) account on your site.
3) Disable the automatic login feature.

I hope that helps explain and gets you going, but should you need anything else, just let me know.

Thanks,
Alex