For something to be a "right," it must be something you have the right and ability to pursue on your own. A right is contained within the self. If you believe in personal property, personal control, personal choice, the end result is a philosophy that rights are individual liberties.
A good is something it is nice to have, but to which there is no inherent entitlement. Goods are purchased or bartered for in some way.
Health care is not a right. You have the right to pursue a healthy lifestyle. You have the right to negotiate for health-related goods and services, but you are not entitled to the services of other people.
We cannot mandate a certain number of medical professionals exist. We cannot mandate that trained doctors treat everyone. A doctor is free to retire and go fishing if he or she wants.
Since health care relies on other people taking actions, to force them to do anything is servitude.
Is there an ethical reason to have national health care? Sure. But that is still not a right, it is a choice that has costs and impinges on the freedoms of those in medical fields.
My "rights" never involve making (or even bribing) other people do things.