Twitter’s board doesn’t have any obligation to maximise short-term profits for investors (or maximise profits generally) - there has always been a misconception that companies/directors had to by law but the actual laws are much more general.

But at the end of the day, if the board thinks that Twitter may be worth more long term than what Musk is proposing to buy it for, then it’s perfectly reasonable to argue that it’s in the shareholder’s interests not to sell it.