In my experience, I’m not sure you’re going to have any success with this.
Ask yourself from both sides of this conversation: “what does the other person want out of this interaction?” How do you think he’s perceiving you right now?
There’s a lot of factors here to consider and questions to ask. You say that you “need to communicate with” him. What does that mean? “Need to for work?” Guess what? At work (my last job, I mean), I used all the garbage communications methods: SMS, Teams, you name it. “The nail that sticks out gets hammered down” or something like that. Pick your battles. There was no way I was gonna convince my company to use Signal (I couldn’t even convince them to get off LastPass), and my ability to put a roof over my head was priority.
If you “need” to communicate with him but risk of getting fired or in trouble is unlikely, how sensitive is the data really? Are you transferring financial documents? Fair enough (see next paragraph). Is it just “run of the mill business stuff”? Again, pick your battles. You may win the battle by getting him to use Signal, but you may lose the war by making him hate you and not enjoy working with you anymore because you’re being so difficult and obtuse. I promise you, there are few things worse (in this context) than being the employee everyone hates. I’ve been that guy and it literally caused depressive episodes.
In the case of the financial documents example, are you hiring him, like an accountant for example? In my opinion, if you’re hiring someone, they need to shut up and do what you’re paying them for or else you need to go find someone else. So if your accountant refuses to use encrypted email, for example, find one who does.
Soft skills are just as important in spreading privacy as the tech is, in my opinion. Not to be rude, but it seems to me like you’re coming at this from a “trying to win the argument” angle. Like Fria said, reframe the problem. Don’t make it “my privacy vs his whatever.” Make it “us vs the problem.” The problem is that you both want to communicate securely but have different opinions on what counts as “secure.” So how can you guys tackle that together?
It may also help toward that end (soft skills again) to explicitly say that you appreciate the options he’s offered. “Hey, I really appreciate you offering things like Telegram and WhatsApp, I promise I do. I recognize that you’re trying to be flexible and meet me halfway. But here’s why I’m worried those services aren’t secure enough for what we’re trying to do.”
Here’s a thought experiment: what are you gonna do if you just can’t convince him? Cause in my experience, you usually can’t. Maybe someday they might be receptive, but right now they’re not for whatever reason. So what then? Are you gonna cut ties and move on? Are you gonna give in and try to be that person in their life that they can go to with questions? Ask yourself that.