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…
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.