Unsurance
My scepticism towards insurance is not entirely misplaced, in fact Urbandictionary has a word defined for it.
Coverage by contract whereby the party which has undertaken to guarantee protection or coverage against loss by a specified peril reneges said coverage when protection or action becomes necessary.
E.g:
I had to take little Throckmorton to a specialist for his asthma, but the visit was not covered by our health unsurance policy.
