Insurance claims and qualms

Within the issue of Insurance companies knowing our medical status, the question arises, "should they have access to our genetic make-up?" In my opinion, if my insurance is affected by what could be a possible health defect or weakness, of course I'd say no. Since, however, they already know medical history and other information, and it does affect our policies, I don't really know what can be done to pursuade them otherwise. It doesn't seem fair that people who may need the insurance sooner are often denied it and that people who are considered healthier have higher access to it. Unfortunately that is the paradox within the insurance industry...