I simply can't bring myself to use unreasonableness, but can think of no synonym or alternate form with comparable meaning.
I'll restructure if necessary, but wonder if I'm missing a suitable alternative.
You could try contrariness, obduracy, or obstinacy.
Here are a few alternatives to "unreasonableness"
How about irrationality, or pigheadedness for that vernacular charm? Incorrigibility could also fit, as could idiocy, although I think those are deviating from "unreasonableness." Megalomania most likely doesn't work, but it's a wonderful word. :)
You could try obstinance for someone being willfully unreasonable or obtuseness if it's more a matter of their nature.