To use your example of emailing the police chief: let's say your threat profile is that you're being stalked by a criminal, and you want to email the police to give them information on this crime, but you don't want the criminal to know. If the criminal breaks into your email, or if your house is broken into and a hidden camera is placed behind your computer, it makes little difference whether you have end-to-end encryption or not, your privacy is still violated. Does that explain it better? Maybe Proton could have some better messaging around this, if their customers are getting privacy and security confused?
Security and privacy are intertwined, imagine your server getting hacked (security problem) leading to your private documents being exposed on the internet (privacy violation).