Medical care, like marriage, should be a matter of equal rights, true. But, like marriage, one’s “right to medical care” does not entail the obligatory services of anyone.
If you cannot find a partner moved by love, lust, or pity, you will remain unmarried. And live alone, until you die. Still, though unmarried, your rights have not been abridged.
If you cannot find a doctor or nurse to aid you when ill or injured, or to advise you when healthy but concerned — if no professional is moved by acquisitiveness, curiosity, or pity — then you will remain untreated. And suffer alone. Until you die.
And your rights have not been abridged.