The fundamental nature of a right is that it places no obligation on anyone else. I have rights by virtue of my existence, or by merit.  For example, my right to life obligates no one to do anything.  My right to property - what I have earned - obligates no one.  Quite the contrary.  Others are not permitted to murder me, nor are they permitted to steal from me.  To recognize my rights, others need do nothing at all. No one's actual rights allow them to trample upon the rights of others.  If what you claim as a right infringes upon someone else's rights, than yours is not actually a right.
Treating healthcare as a right undermines the very essence of actual rights.  If healthcare is a right, then healthcare workers are obligated to give it to you for free, no?  Or, at the very least, everyone else is obligated to pay for your healthcare.  But what about everyone else's right to their own freedom and property?  Progressive misinterpretation of rights is nothing more than tyranny.