You can unsend individual messages for everyone by tapping and holding the message, selecting "Remove," then "Unsend for Everyone." Note: you cannot delete entire chats from both sides simultaneously; only individual messages can be unsent.
To delete Messenger chats from both sides, open the conversation, long-press the message, tap "Remove," then select "Unsend." You must do this for each message individually; there's no way to delete entire chats from both sides at once.