Basically, the problem is that they invented a lot of their own crypto from scratch. When asked about this, they said "it's fine, we're smart" and then claimed to prove their security with a red herring contest.
Here are some publications about security problems with the platform:
- A class project at MIT found several problems (May 2017) [0]
- They were featured on Crypto Fails (Dec 2013) [1]
- Jakob Jakobsen @ Aarhus University published a vulnerability discovery (May 2015) [2] and then did his Masters thesis on additional problems (Sep 2015) [3]
-Tomas Susanka @ Czech Technical University in Prague published additional vulnerabilities (2016) [4]
Moxie might have his own horse in the race, but his analysis of cryptosystems should not be questioned. His philosophy is around humans being able to access strong encryption.
I believe he ultimately doesn't care what you use, as long as your communications are secure.
I haven't used Telegram in a while (so maybe things have changed since then), but I would guess that that grandparent is talking about how they rolled their own crypto, and how secure conversations isn't the default setting
Supporting sources?