I also never meet anyone who has such an extreme view on things.
Here in Europe, we believe that certain things should be public: education, roads, health care, social security, basic research, while other things should be private, like smartphones, cars, ...
And I think for most of the things we like public, there is a good evidence that it should be. I.e. Euro style health care systems spend less money per patient while achieving a higher average lifespan when compared to whatever system the US has.
In general, the argument for private systems is that since they have to make a profit, they will be more efficient. In reality, they have to make a profit, which public systems don't have to. Public systems however have the same price pressure than private systems, since people put this pressure up via democracy.
The biggest issues I see is that public systems are less capable of big innovation vs. small process improvements. This can be tackled via the basic research done at public universities + the private sectors work to bring these to market.
Also, if you follow Peter Thiele Line of thought on how every business should strive for monopoly, so they can take monopoly profits and "focus on the product instead of the competition" - a public service that has granted this monopoly by law would be perfect: they have no competition, so they can focus on making the best product, and they don't have to make a profit, which means they can operate at cost.
Now, I don't think it's as easy as that, but in the end, if you stop being an extremist, you can mix and match all kinds of system to use what is best, instead of striving for something that is ideologically pure.
tl;dr: I want my smartphone from private companies competing for the best product, I want my water from a public utility.