You used to sign on Facebook but got rid of it. Now it shows back up some how showing you to sign on using Facebook. Somebody thinks you still have an account.
So what can you do about this? Somebody sees that you have been on Facebook when you have not been signed in quite a while. Facebook won't remove or deactivate your account unless you request it.
You can check out Facebook's how do I delete my account page to either deactivate your account temporarily or submit a delete request. Even if you haven't logged into your account for a while, people will still be able to see your Facebook profile. According to Facebook, some items that are not stored within your account will remain ie. messages you sent to somebody else.