There are a very few things that simply can’t be run on a fully private basis, and the armed forces certainly fall into that category (though a huge percentage of the money spent on our armed forces goes to private companies producing equipment and providing services on a competitive basis). Postal service is not so clear, though I believe international agreements governing cross-border postal service make it next to impossible to fully privatize postal service. However, the postal service in the US has been subjected to intense competition from private delivery companies, which now handle the great majority of package deliveries, and from thoroughly private Internet communications, which now handle the great majority of written correspondence.
Medical care can easily be run on a fully private basis, and has been in the past. Choosing to have government run something that could clearly be run privately is socialism. And the engine behind the “choice” is politicians using tax revenues confiscated from the more productive members of society to buy votes from the less productive members of society, who want to make other people pay for their medical care (and all sorts of other things) while they continue being unproductive.
Here in NZ our postal service is run on a competitive basis. Anyone can start up and operate a postal service here, if they want to. Many have tried, most of them suck. The government-owned NZ Post is by far and away the best — probably in the entire world.
What it comes down to is this: what services do the citizenry want the government to deliver as a matter of National Priority? Those services are “socialized”. All the rest is “privatized”.
It is possible to run a privatized Armed Forces successfully. Lots and lots of countries have used mercenary forces to defend them. The Vatican still uses the Swiss Guard: they were once a mercenary force. They are still “outsourced” from Switzerland.
It all comes down to national priorities. Just because a service is “socialized” doesn’t mean that it is necessarily a byproduct of “Socialism” as an ideology.
Ideology does not need to play any role in that decision.