Should you have an issue with login with facebook on our website, do check and see if your cookies are enabled. If it is enabled, do try to clear the cookies. On a windows PC, press Ctrl-Shift-Del and select cookies.
If still having issues with login via facebook, do adjust your privacy settings with your anti-virus product. Known products such as Kaspersky may block our site from accessing facebook cookie which would allow the login accordingly.
Alternatively, setup a normal login via request for a 'I have forgot my password', and it should email you with a password. Do wait for some time for the email to arrive, if not check junk or spam folders.