The so-called social healthcare as pushed by the government will inherently waste a lot of money because government is always wasteful with it's resources. Governments are wasteful because whenever they run out of money they have the option to tax people more. On the other hand companies that waste a lot of money will eventually be removed from the marketplace, as they are unhealthy. This is one reason why healthcare as a government responsibility might be a bad idea, because whenever money is badly used in healthcare, instead of fixing the actual issue the government is more likely to just tax people more.
I think many opponents of social healthcare feel it should be an employees responsibility to spend the money as they think is best. If they want to spend a bigger part of their earnings on healthcare, they should be able to and if they want to spend nothing at all they should be able to as well.
Proponents of social healthcare will argue that some people don't know how to spend their money wisely and as such they will find it's a task of the government to make sure a part of the earnings will be forcibly spend on healthcare. It should be understood that this will inherently remove some (financial) freedom of the employees and perhaps from the employers as well.
Here in the Netherlands social healthcare is financially becoming more and more expensive. One big issue is that people who are forced to spend part of the earnings right now won't be sure they will actually see any of it back in 30+ years when they grow old enough to need healthcare themselves due to our society having more and more ageing population and less young people to support the healthcare for this ageing population. We've pretty much got the same issue with our socialised pension plans.
If young people would be able to save some earnings for their own healthcare, they could have a better guarantee being actually able to use it when they grow older.
The book "The Road to Serfdom" by F.A. Hayek explains why many socialist measures (even with the best of intentions) often risk pushing government into the same dangerous direction that Russia and Germany went in the past: http://www.tiptopwebsite.com/custommusic2/mrsilber2.pdf