A Discord is a public space. For most users, hanging out in Discord is akin to hanging out in your local bar. No once cares too much that anyone at the bar can see everyone and overhear all of their conversations. If anything, I am there to be in a public place. The tables are nice and the drinks are cold. And if the owner sees we are unhappy and having a bad time, and uses that information to improve the bar, so be it.
Even if Discord guaranteed absolute privacy, they can't guarantee that some other users is not just scraping the conversation and reposting it somewhere. The danger of "privacy" is when people are being mislead about how alone they are. But just falling back onto a "more private = more gooder" is not an actual argument about risk associated with using Discord.
You can try to convince your friends to go to a worse bar with worse service strictly on the basis that it's more private. And maybe that's a good argument for your friends or your context! But you can't actually assume all of your friends are only going to care about that.
It's not as convincing an argument as some people think it is to run into a Discord server where hundreds of users and moderators are having very public conversations, yelling "none of this is private!", and expecting them to care.