Besides being the best way to contact you, the most effective way to convince people to switch to Signal is to try to appeal to features they’d find useful. There’s a thread on Privacy Guides where people brainstormed some of its other benefits but I’d also search this forum to be sure you don’t miss any.
I have dealt with these people before. They’re so paranoid about nothing being “truly secure” and their foolishness results in them choosing worse options than your proposed alternative. I’d agree with everything @BiggishDoctor said and I’d try those arguments out. If the security angle fails you can also try to promote Signal from the angle of free software which has benefits beyond security.
(Open for a tangent on Signal & free software.)
Signal isn’t ideal if free software was your primary concern but you shouldn’t get into that nuance with them. On the off chance they call out Signal for having shortcomings, AFAIK SimpleX Chat should be a 100% free/libre alternative while being even more secure/private than Signal. The paranoid friend might also appreciate it not having a phone number requirement.
The main downside is that SimpleX Chat might not be as easy to use or feature-rich as Signal at the moment. I haven’t used it in a long time but Session might be easier to use than SimpleX Chat considering it’s more mature, just keep in mind it isn’t as secure as Signal and is no longer recommended by Privacy Guides.