Yeah, this is like Hotels.com suing random hotels.

Worth noting the "They won’t let us compromise by using a different case, an ampersand or an ‘and’" bit - so it's not just bnb which they claim to be infringing, it's also BnB and B&B.

Companies House lists thousands of businesses using those letters, and there'll be many more which aren't limited companies. Plenty of them will predate Airbnb's formation. Despite the difference in legal firepower, I suspect Airbnb might find it hard to win this one.