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.

yup, also you can trust the person but maybe not trust their long term security. the short the lifespan the small surface of attack.

Depends on "they", I guess. Plausible deniability goes south, once you are greeted with a wrench. Reminds me of https://xkcd.com/538/