Why it always breaks

It is about the shape the four bonds make. Follow them from word to word: king needs queen, both royal. queen needs woman, both female. woman needs man, both ordinary. And man needs king, both male, which puts you back where you started.

That is a ring. Four words, four bonds, closed end to end with no first one and no last.

Picture it as beads on a bracelet. Every bead touches the two it belongs with, and a loop has no ends, so no bead is stranded.

Now unclip the bracelet and lay the beads out in a straight row. Two of them have to land at the two ends. An end bead has one neighbour instead of two, so a bond that was short on the bracelet is now stretched across the entire row.

That is the whole reason. A row has two ends, a loop has none, and flattening one into the other always costs exactly one bond. Cutting the bracelet in a different place only changes which bond you lose, which is exactly what you felt happening.

So this was never about picking better numbers. We could fiddle with the exact values forever and never fix it. The line itself is too cramped. It offers one direction to spread out in, and meaning pulls in more than one direction at once.