Blog post by crypto professor Matthew Green, discussing what Telegram does (I wasn’t familiar with it) and criticizing its cryptography. He says Telegram by default is not end-to-end encrypted. It does have an end-to-end “secret chat” feature, but it’s a nuisance to activate and only works for two-person chats (not groups) where both people are online when the chat starts.
It still isn’t clear to me why Telegram’s founder was arrested. Green expresses some concern over that but doesn’t give any details that weren’t in the headlines.
We really don’t need more than #3 for a reason to stay far away from Telegram. Security through obscurity is not security, and neither is rolling your own crypto.
Just note that the comment was inaccurate, in that their weird encryption is indeed open source at least.