The notion that your direct messages with someone are private is something that I think is generally misunderstood, I don't know if many non technical people realise that there is no reason that Facebook can't directly read your messenger or Instagram conversations, as if they were posted publicly on your profile, and I think if they did, they might treat those platforms differently, or think twice before discussing the more sensitive aspects of their lives.
The problem is, having a DM be what it says it is, a direct message between two people, unreadable by anybody else, *requires* end to end encryption, nothing less.
The thing is, there are some noteworthy tradeoffs you have to make to fully embrace using end to end encryption.
If you're using an encrypted messenger like Signal, Wire, or WhatsApp, you'll quickly notice that unlike your Instagram, Facebook, Telegram, or Discord chats, you can't just log in on a new phone or computer, and see all of your chats, just as they were, waiting for you to reply to that last message, with all of the chat history for you to read through right there.. because the reason you've ever been able to do that before is that your messages have lived somewhere on a Facebook / Telegram / Discord server, unencrypted, ready to be sent to any new devices you connect.
The difference on Signal being that your messages are not kept on any central server, they're kept on your phone, and only your phone.. so when that phone breaks, or gets replaced with a new one, when you log in to Signal you're greeted with a blank inbox.
This means that the idea of keeping your chat history between device changes involves maintaining backups, and ensuring that these backups are kept up to date, and encrypted (what's the point of having encrypted chats that are stored in plain text backups? Looking at you WhatsApp).
(or as much of it as you want to keep)
So say you've been using Signal (or any other encrypted messenger) for a few years, you've got some group chats going, you're sharing memes with a few friends on a daily basis, before long there's a few gigabytes of data being stored by this app, quickly it's the #1 user of disk space on your phone (or maybe second to your photo album), and those backups that are happening every week are doubling this number.
The idea of maintaining this ever growing history of your conversations becomes harder and harder to care about, as the amount of data gets larger.. so what's the answer?
You can embrace ephemerality as Signal recommends, and have all of your messages disappear after a certain amount of time (hell, that's like Snapchat's main selling point), this keeps the amount of data you need to manage relatively low (or you can forget about managing it completely, turn off backups, and be happy with everything disappearing if you change phones).
Or you can get a nice big SD card and brute force the storage problem.
Or you can just give up on your privacy completely, and use another app where you don't need to think about these kinds of things and everything just works™.. for example Telegram, which works very similarly to Facebook Messenger, has unencrypted chats by default, with the option to go into encrypted "secret" chats if you want to speak privately.
Maybe this isn't a bad idea, if you trust the company running the messenger platform not to spy on you too egregiously (read: not Facebook), you can give them the ability to store and decrypt them for the sake of your convenience, and just go into a secret chat for anything that you want to be just between you and the person you're messaging.
I'm kind of torn on this, because while I do believe that privacy and encryption should be the default, I also occasionally find myself looking at my old Facebook Messenger conversations, reading chats with people that I haven't spoken to in years, cringing at how I used to speak, and just checking out what kind of things I used to talk about or be interested in.. is that normal though? To go over conversations from 10 years ago, to have the words that I spoke then readily accessible to read at any moment?
Maybe it's better to have to go and sift through old backups to see that kind of thing, rather than trusting an unknown third-party to "keep it secret, keep it safe" for me.