1. It makes your data harder to compromise
Using two-factor authentication adds an extra layer of protection for your accounts. It's like having a regular lock and a deadbolt on the front door of your home, or locking your car, but also engaging an alarm system. The idea is that an attacker may compromise one of your authentication methods, but probably won't be able to compromise both. Just the fact that you have multi-factor authentication in place at all serves as a deterrent, because attackers will generally move on to easier targets rather than investing the time necessary to access your accounts.
2. It prevents fallout from a data breach
If you use two-factor authentication, you have much less to worry about from the data breach du jour. A website you use might get compromised, or a retailer you frequent might be the victim of a network hack, but the data gleaned from the breach is only one of the factors. As long as you also use something you have or something you are as additional layers of authentication, your identity and data should be safe even if your passwords or other personal data are exposed in a breach.
3. It can alert you to break-in attempts
Two-factor authentication lets you know when there are unauthorized attempts to access your accounts. If you suddenly receive a text message with a code, or an email verification when you aren't accessing the account yourself, you can assume that there is some sort of suspicious activity. Your account should be safe because you have two-factor authentication in place, but if the attacker was able to get to the point of triggering the two-factor authentication it probably means your username and password are already compromised, and you should change your password immediately.
It's an imperfect world. Even in a best-case scenario there will still be security issues and data breaches. Don't surrender security in the name of convenience. Take advantage of two-factor authentication for any devices, sites, or services that you can so you can make sure you're protected even when nobody else will.
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