Critics of socialized healthcare often point at things like waiting too long for specialists, or understaffed hospitals, presenting them as inherent to socialized medicine itself when it's more often the product of elected officials who simply don't think socialized healthcare deserves adequate funding, or are against the idea of socialized healthcare entirely. Politicians will often piss in your cup and insist to you it's champagne.
There is, of course, the economic arguments around public vs. private health-care systems; but there are also the philosophical, moral, and ethical, arguments regardless of economics. Some things are expensive and yet we still understand they are a good and humane thing to do.