I don't understand. If I'm in an abusive relationship or am a whistleblower why would I want to send a read-once message? Why is this better than pastebin? (Which, incidentally has this as an optional feature)
If you trust the recipient, but there's a chance that they will be threatened and asked/forced to reveal the message that you sent them, they may appreciate a mechanism that gives them plausible deniability.
Obviously a recipient could make a copy of any disappearing message that they receive if they really wanted to, so you do need to actually trust them. It's less for your security, and more for theirs.