False argument. Healthcare can’t be a right because it is a vaguely defined term. Part of that is the fact that it is supplied by nurses and doctors so where do their rights end so that you can have your right to healthcare. It isn’t slavery and nobody honestly makes that claim. Though doctors and nurses in some countries with “universal care” get paid about what we pay postal workers. That would have an impact on quality.
Universal healthcare is also a vague term. If you are trying to claim that universal healthcare means that everyone will get every treatment they think they need then what you are selling is a lie. Our current system is already around 50% paid by the government. The government pays that 50% for just the elderly, poor, and current/former military. The other 50% is mostly paid to private insurers, which are regulated by the government, with a small amount of out of pocket costs in there also.
What is fixed by changing our 50% government funded healthcare system to 100%? Consumers get benefits from having private coverage. They can choose between competing companies and when they do have a dispute they can take it to the government. The government controls the insurers by finding them and threatening to fine them on claims that they should have paid. Who do you go to when the government is the insurance company and they refuse to pay your claim? Do we believe threat the government will be more efficient somehow in managing the whole system? How could we possibly believe that given the current system where they pay 50% of all costs with far less than that many of the people? What incentive would they ever have to do better?
Universal healthcare via the government is a fantasy at best and an outright lie if we are being honest.