I am guilty of the "Fuck you" one. The offered terms insulted me so much I no longer wanted to do business with the person. Had I taken this article's advice, I would have stayed calm and moved toward some highly unsatisfying "middle ground" purely to "close the deal". We are faced with innumerable opportunities in our lives, and we need to filter out the best ones; for most negotiations, a successful outcome is not…
They may simply be trying a hard-ball negotiation strategy, while being able to afford to go a lot higher.
The best thing you can do is to explain that their offer is worse than nothing for you and there is no way you can go ahead with it (but don't tell them your break-even point), and collect more information about their situation - understand why they want to do business with you, try to understand it from their point of view: how much revenue can they make from what you have, and what their costs and revenues for substitute options. If they won't get as much revenue from the deal as what your costs will be, then it is not possible for you both to make a profit and you can part amicably without doing a deal.
If they would bring in a lot of revenue because of the deal compared to their next best option, you can offer them a price which splits the profit for mutual benefit.
Collecting the information needed to see it from their point of view is hard and takes tact, but it is the most important part of negotiating.