16 March 2020
UPDATE (November 27th, 2019):
It is time for another screenshot shared by WABetaInfo folks confirming that WhatsApp is indeed working on self-destructing messages functionality. The feature is called Delete Messages which can be enabled and disabled at the user's will. When enabled, there are various time durations to choose from 1 hour, 1 day, 1 week, 1 month, and 1 year. It is the time after which the message(s) will get deleted automatically.
The feature is currently available in the beta version and was spotted on WhatsApp version 2.19.282 meant for Android devices.
Original (October 2nd, 2019)
WhatsApp has started testing self-destructing messages with the latest beta version. The feature was spotted by WABetaInfo which has an exceptional track record related to features WhatsApp is working on. It was visible on WhatsApp beta v2.19.175 but is not available for everyone using the version.
The WhatsApp self-destructing messages feature is bare-bones at the moment. It allows time limit to be set at either 5 seconds or 1 hour after which the messages will be deleted automatically. The good thing is that the feature is available for group conversations as well. The team is referring to the feature as "Disappearing Messages" which is disabled by default.
The ability to send self-destructing messages can be helpful for users in various situations whenever they don't want a piece of information to stay forever in the conversation thread. This particular functionality is already available on Telegram, one of the biggest WhatsApp rivals. Telegram offers Secret Chats feature where it allows setting a time limit for the whole conversation. It further prohibits the forwarding of texts as well as screenshot capturing.
There are no words on when WhatsApp will expand the functionality of sending self-destructing messages to everyone. By the time it happens, we can expect the team to refine the feature as well. We will keep you updated as and when it will happen.