Assuming I read this right the insuree buys insurance from the insurer for price P and then sells the insurance immediately to the anti-insurer for price P'. The problem is this price P' would be guaranteed to exceed the expected return.

Intuitively for the insuree there exists some prices P' and P for which Eu(P'-P+r_asset) > Eu(r_insurance + r_asset - P) [1]. r_asset is the random return on the asset being insured (medical debt, car damages, etc). What we want to show is that E(r_insurance)<P' [D].

A simple insurance model would have r_insurance = -r_asset (all losses are insured 100%) and P > E(r_insurance) i.e. the insurer turns a profit. Assume it is profitable for the anti-insurer, then we would have E(r_insurance) > P'. The RHS of [1] becomes Eu(-P)=u(-P) and we have Eu(P'-P-r_insurance) > u(-P). This is a certainty equivalence meaning under a risk-averse insuree we have -P < P'-P-E(r_insurance) implies 0 < P'-E(r_insurance) and E(r_insurance) < P', which is a contradiction. So as long as the insuree is risk-averse this will never be profitable.

This could be wrong but 5 minutes of manipulation seems to clear up why there's no such market.