The problem is one of paradox. There cannot be an inherent right to something that requires the labor, materials and ingenuity of others. Such a position would render health care providers slaves to the rest of us.
Same goes for food and shelter. If these things are a right that I am due, then why should I work for them? I’d sure like to just pursue hobbies all the time…
I believe we must change our point of view and instead of using the rhetoric of “rights” to describe these things, we must go back to the idea of a ‘duty of charity.’ The poor don’t have a ‘right’ be be handed these things, the rest of us have a duty to help them help themselves. That’s inherently different in character.