Two questions.
My family insist on using Whatsapp for the family chats. I have to keep a copy on a device just so I can communicate with them. I do so under protest, as I was always told it isn't secure. My brother has just said
"oh Whatsapp is encrypted, it's perfectly secure".
First, is it actually as encrypted and safe as my brother claims? That would solve everything.
Second, if it isn't, where can I get some proof that we should switch to Telegram or whatever? Proof which doesn't make me look like a raving loony?
That's true in the sense that if a very sophisticated organization directly targets your family chat for surveillance, they're going to find a way to access its content no matter what communication method you use.
Threat modeling is core to security, and that kind of threat probably isn't the issue here. Mass surveillance, both government and corporate is, and neither is likely to secretly install malware on a family-members phone that can access the contents of the group chat. Doing that to large numbers of people would get them caught; they save it for valuable targets.
Governments openly forcing the install of spyware, as I've read China does in some cases would be an exception; you cannot have a secure conversation involving a device so compromised.