The idea that health care is a right flows directly from insurance.
Insurance is a contrivance for regulating health care expenses. Policy holders pay a regular premium into a group pool. When they have an irregular medical expense, they file a legal claim against the pool.
Paying a premium into the pool gives policy holders a right to withdraw resources from the pool.
Yes, I intentionally emphasized the words "regular" and "claim" to emphasize that insurance is a scheme to regulate health care through the legal system.
The rights involved with insurance are conditional rights. It is on the condition of paying the regular premium into the pool that people receive a right to the resources of the pool.
This conditional right, however, leads people down the path of thinking of health care in terms of rights, and eventually into all of the logical pitfalls that occur when one tries to claim health care as a human right.
For libertarians to turn the conversation around, they must work to create alternatives to insurance. The most promising alternative is the Medical Savings and Loan. The MS&L uses a combination of savings, loans and grants to pay for care. The system has people paying a premium to give access to medical loans. However, it is a step removed from the concept of health care as a right as it has evolved in the insurance world.