Maybe you could try to convince through other features, like sending sharper images, videos, audio messages or video calling etc.
If you get closer with her friend circle (or if she gets closer to your friend circle), you could propose to make a group chat, where you can keep each other up to date or plan future activities together. Your wife will probably not want to miss out on that.
Don’t talk about encryption or security to normal people, who are not into tech. They do not care. Only talk about features, that they can actually use, and only in situations were this would be useful. Don’t be preachy about your messenger use, don’t make them feel stupid.