Mark Zuckerberg was caught out earlier this when it was found he, and other high-level Facebook execs, had the ability to erase messages they had sent to other people's inboxes. That feature will be extended to the rest of the world according the list of "Coming Soon features.
The Facebook Messenger app for iOS App Store entry has been updated with the following note:
Coming soon: Remove a message from a chat thread after it's been sent. If you accidentally send the wrong photo, incorrect information, or message the wrong thread, you can easily correct it by removing the message within 10 minutes of sending it.
Ten minutes seems like a reasonable time period. In my experience, you know pretty quickly whether you've sent a message to the wrong person (or the wrong message to the right person) most of the time.
Google supports an unsend feature in Gmail although that works a little differently as it holds a message for 5, 10, 20, or 30 seconds during which you can change your mind.
While there's no ETA on the message removal feature, it seems to be tied in with the redesign of Messenger that Facebook recently announced. Unfortunately, encrypting messages by default, like Whatsapp, Apple Messages, Signal, Telegram and other services isn't on the roadmap as far as I can tell yet. However, there is a "Secret Conversations" option in Messenger that does encrypt messages but you need to turn it on for each conversation manually as it's not enabled by default.