This reminds me of the long conversations that I used to have with family members and friends several years ago. With their continuous requests to create my own Facebook profile so I can keep in contact with them and with their activities as well as to share my whereabouts. I always used the same argument to reject these suggestions — "I don't want Facebook to have too much data about me, more than the data that you…
Isn't it still trivial to self-host stuff?
Just send a link to picture (or document or whatever confidential information you want to share) to a password-protected resource on your own server (or even a laptop or desktop machine, if you have globally routeable IP address there). Facebook automation is not that smart to grab the password from the very same conversation, and even if they do - I'm sure they won't do it, knowing you'll catch them in access logs and press charges for unauthorized access.
I doubt many would object and insist on sending via a very specific medium (i.e. strictly require pics in a FB Messenger). Some, of course, may find this inconvenient.