You're opposed to the idea of universal healthcare? Really? The concept that everyone has the right to quality medical care? Do you really believe that all those folks you volunteer with don't deserve medical care?
There's a limited amount of health care to give because there is a limited amount of people willing to provide it. There is no concept of "right to health care" that doesn't require slavery.
You can argue for universal health care but arguing that people have "a right to health care" makes no sense.
Imagine there is 1 doctor. Doctor doesn't want to treat patient (could be sick, could be tired) but patient "has a right to health care". The only way to honor that right is to force the doctor to treat them.
I'm not sure how "every government worker is a slave" fits. The things most government workers do have nothing to do with "rights". As an example there is no "right to protection" even though we have police. There are rights that prevent the police from doing bad things but there is no right that forces police to help anyone.
What said was claiming people "have a right to healthcare" requires slavery.
Universal Health Care != "right to healthcare"