The Real-time Protection function of Avira Antivirus for Mac is designed to detect phishing and backdoors so that you are protected against these kinds of attacks.
There are exceptions like, for instance, if a hardware logger is attached to your computer (usually between the keyboard and the computer). This can’t be detected by any software but can be seen easily and can only be installed by someone who has direct access to your PC.
Secondly, it can happen if communication between your computer and a third-party site is not encrypted. This can be logged by anyone who has access to your network infrastructure. That’s why communications with your bank are always encrypted (HTTPS protocol).