What chauvinists call the ability to act like a "lady" in the Victorian sense, which includes only speaking when spoken to, being dainty and submissive to men, and humiliating other supposed "ladies" in order to make oneself appear more ladylike. "Ladybility" is a portmanteau of the words "lady" and "ability."
Man 1: "Sir, I would like to introduce you to my date to the party, Lady 1."
Man 2: "Pleasure to meet you, Lady 1. How do you do?"
Lady 1: "Quite fine sir, thank you. I'm just a tad lightheaded from all this manly discussion. Did you notice that lady in the corner who just burped? What a mannish sort of woman!"
Man 2: "What an impressive ladybility you have, my dear Lady 1!"