I am really interested why Signal. Why not Telegram? I prefer Telegram over Signal because of much more better UI and rich functionalities i.e. bots. Signal app seems clunky and buggy. That's my 2 cents.
Telegram does so by default, you have to opt in to keep messages private from the server.
You also see a lot of people criticizing the design of the secure Telegram protocol and praising the Signal protocol. There were some stories about governments actively compromising Telegram's security. There haven't been any about Signal.
So if you are worried about privacy more than UI and rich functionality, the choice seems clear enough.
You can use secret chats, those messages are not stored on the company server.
For messenger to gain a MASS of users it has to be 'enter sms-code and go chat'.
For messenger to be SECURE it has to be 'install password manager, set passcode, use 2-factor, use e2e, use self-destruct, always compare keys'. No one will enjoy that. But if you need, you just have it in your regular sexy messenger, not in another ugly alien app that no one knows about, no one has installed, no one's ready to go through all of it.
I think telegram guys got it just right.
[1] https://telegram.org/blog/15million-reutersThe unencrypted messages are certainly not secure, and it's disingenuous of Telegram to market itself as a secure system without being really clear about the limitations.
And I would be really interested to know why people are downvoting a perfectly reasonable question.