Are you linked to the net? Haha, seriously however, are you?
Thinking you have the best login e-mail and also password (and you're attached to the net) there's a couple of points that might be causing your troubles:
Trouble Logging Into Facebook
Are you obtaining an error message? If so, check the Facebook help page for descriptions and also fixes to well-known issues.
Make sure you don't have any extensions or antivirus programs running that are obstructing Facebook.
Have you tried removing the application's cache? Go to Settings > Applications > Facebook > Clear Cache. If this does not function you can try clearing up data too and as a last option uninstalling and re-installing the application completely.
Did you join your phone number? Ensure you key in the country code as well when logging in.
If the app is telling you to upgrade your email address, this is probably because your email web server is labeling your Facebook e-mails as spam.
If you've just recently signed up for Facebook you might need to validate your account first. If you've recently changed your password, ensure you're trying to log in with the new password and also not the old one.
If you're logging in using a web browser, ensure you have cookies allowed which facebook.com is added to your list of safe sites.
Make certain you have the most recent variation of the Facebook app for Android.