It is difficult to explain people outside the tech-community why encryption is important, but John Oliver mastered this challenge.
Every time there is a brutal crime, politicians again demand government backdoors for encryption software. Realising the consequences of those demands often takes politicians and the public a long time. Encryption helps all of us to keep us safer against criminals. Government backdoors might benefit security in the short term, but lead to security nightmares for all of us in the middle and long run.
Demonstrating the implications of backdoors is hard. But in his last show, John Oliver made it, and illustrated the importance of encryption (youtube). Those 18 minutes will most likely help you to improve your argumentation for encryption. So definitely worth your time.