Authenticators normally work very well and are great to have on your account. Removing it is not wise. What version do you have, mobile or keychain? Are you able to log into the web site but not the game?
If Mobile you have a few options:
1. Be sure you properly attached it to the account. https://us.battle.net/support/en/article/battle-net-mobile-authenticator-faq
Install instruction video is there.
2. It could just be out of synch. In the application menu, use the resynch feature. Instructions are in the link I just gave
3. Be sure you are entering the proper information during login - retype the email address and password by hand, not auto fill. Then be sure you are entering the Authenticator code within the 30 second window it is good for.
4. If that fails, you can try re-installing the application. To do that, write down the serial number and restore code
. Then delete the app, download, and install again. When done go to the app menu and use the Restore feature then resynch it. Details of how to do a Restore are in the link above.
Last but not least, there is some malware out there that can block the Authenticator code from being sent and give you a fake error message. It tries to trick you into removing it. The biggest symptom is being able to log into the web site but not the game. One way to check is to do the following
1. Download, install, and update Malwarebytes (free version is fine). Boot into safe mode and run a FULL (not quick version) scan with the game up and gibberish in the login fields. Some malware only activates under those conditions.
2. When that scan is done, run a FULL virus scan with an updated virus scanner. Microsoft Security Essentials is free and decent these days. Better than Nortons, MacAffee, etc.