Some poor people, in fact, may obtain better care under socialized medicine. But many in the middle class will lose. It isn't clear where justice is to be found in such a redistribution. We may let private initiative and voluntary relations provide solutions. Or we may let politics decide.
Health care has to be rationed either by the market or by political and bureaucratic processes.
The latter are no more just than the former. We often forget that people who have difficulty making money in the market are not necessarily better at jumping queues in a socialized system. There is no way to supply all medical services to everybody, for the cost would be astronomical. Paradoxically for a socialized health system, the family had to appeal to public charity, a more and more common occurrence. This is only one instance of health services that could have been covered by private health insurance but are being denied by hard-pressed public insurance.