the better answer is that there is logic and some passion mixed in here.
the logic part is this: Bacon is in the canon. He has a set place on the list of, say, the 100 most important artist of the 20c. very few paintings become available for purchase from people on that list. When they do, lots of people want them as the centerpiece of their collection. Plus, the subject of the painting is another artist - lucian freud. Freud isn't on the 100 best list, but maybe the 200 best. That sort of incestuous painter - painter relationship always boosts prices. You get two for one, sort of. And it feels a little like an investment.
the passion part is simply that this is art - people fall in love with pictures and are willing to pay extraordinary amounts of money to own them. Bacon has been a hot artist for a while now - people today love his pictures.
finally, keep in mind how much money billionaires have. Let's say the guy who bought this has $10 billion. This painting cost him 1.5% of his wealth. For a regular guy with $500k to his name...that would be like the regular guy spending $7,500 on a car. not crazy.