No closed-source E2EE client can be truly secure because the ends of e2e are opaque.
Detecting backdoors is only truly feasible with open source software and even then it can difficult.
A backdoor can be a subtle remote code execution "vulnerability" that can only be exploited by the server. If used carefully and it exfiltrates data in expected client-server communications it can be all but impossible to detect. This approach also makes it more likely that almost no insider will even be aware of it, it could be a small patch applied during the build process or to the binary itself (for example, a bound check branch). This is also another reason why reproducible builds are a good idea for open source software.
With all due respect to Stallman, you can actually study binaries.
The claim Stallman would make (after punishing you for using Open Source instead of Free Software for an hour) is that Closed Software (Proprietary Software) is unjust. but in the context of security, the claim would be limited to Free Software being capable of being secure too.
You may be able to argue that Open Source reduces risk in threat models where the manufacturer is the attacker, but in any other threat model, security is an advantage of closed source. It's automatic obfuscation.
There's a lot of advantages to Free Software, you don't need to make up some.
>Detecting backdoors is only truly feasible with open source software and even then it can difficult.
This is absurd. Detecting backdoors is only truly feasible on binaries, there's no way you can understand compiler behavior well enough to be able to spot hidden backdoors in source code.