Always three out of four

However you shuffled them, you got three of the four. Never all four.

Take the most natural order: king, queen, woman, man. Walk along it. King beside queen, royal pair intact. Queen beside woman, both female, intact. Woman beside man, ordinary pair, intact.

Three out of four, and the arrangement looks tidy. But look at the two ends. king sits at one end and man at the other, as far apart as four things can be, and those two are supposed to be a pair, because both are male.

Rearrange to fix them and you do not remove the problem, you relocate it. Put king and man together and something else gets flung to the ends. Whichever order you try, you land on three, and all you seem to get to choose is which pair loses out.

At this point you might reasonably suspect you just have not found the right order yet. You have not missed it. There isn't one, and the reason is not about these particular words.