Protonmail claims to automatically send end-to-end encrypted messages between all the Protonmail users. They claim that they do not have access to user’s private keys (Someone having access to your private keys can decrypt and read all your encrypted messages), by encrypting the user’s private keys with the hash generated by user’s password (which is known only to the user). The problem with this is: how do we know that Protonmail does not keep a copy of user’s private keys with themselves before encrypting it with user’s password hash? Also, we cannot really inspect the web application we use in the browser because it is not installed in our own devices, we are using it from Protonmail’s computers.
There is no need to trust server for email encryption. Email encryption can be done within the app. This method encrypts mails within the app before sending it to the server. Here is a guide to encrypt mails using pEp app. pEp encrypts mails very easily. You just have to send one mail to a pEp user to exchange keys and after that, all emails will be encrypted by default. Email encryption used to be hard to use, but it is no longer the case. pEp project has made email encryption (it uses OpenPGP) easier so that nontechnical people also have access to email encryption.
This is the main problem with Protonmail. When it comes to encrypting emails, there is no inherent need for the user to trust the server side for encryption, yet their whole model of encryption lies in trusting the server side. We cannot inspect their server side. We cannot inspect what they run or how they implement all this in their own computers. You can, however, inspect the app running in your own device if the app is free software.
Conclusion: Email encryption does not require user to trust the service provider. Users can encrypt emails in their device before sending the mail. Protonmail is making their users trust the server side for email encryption without any need for that. I advice against using emails from such email providers and instead use email providers which allow you to use independent app like pEp, Thunderbird, K9 Mail, so that you can encrypt emails before sending it to the server.