One example on a smaller scale would is a group project in a classroom (it's fine to assume that this takes place in a private school, otherwise all of the following would be a funny sort of convoluted hahaha).
Let's say there are 30 students and 6 groups of 5 kids each, and they are tasked with some project (maybe a science experiment & report, for example). Each member of the group is to receive the same grade as the rest of their group. Of course, projects like this actually exist, and for good reason, since we all need to learn how to interact with each other and work as a team. This is highly socialistic in nature, and I think everyone agrees that it is overall a very good and very necessary part of our development. There is certainly an element of capitalism, too, since it is known to the entire group that a satisfactory grade will not be given if No One contributes high-quality work. One of the main things I wish to show here is that this is not a black-and-white all-capitalism vs all-socialism scenario (and neither is our society).
It would be nice if all members of the group contributed a similar amount, but I think we all agree that that is an unrealistic expectation. I admit that this is a separate problem on its own, but with the zillions of factors and variables that come into play (even with humans who have only been alive for maybe 15 years), it's simply too much to ask. At least it's out of reach for the foreseeable future. However, there is a wonderful self-policing mechanism built into this group. Each member has access to information such as what things the other member has contributed, and they can even directly observe fellow members during class time. So if Sarah notices that Katie isn't "carrying her weight" (think: "behaving in a socially responsible manner"), Sarah can first speak to Katie directly. And/or she can discuss her concerns with the entire group (arguably the best route). And/or she can take her issue to the instructor (also not a bad route, since the instructor is only tasked with 30 individuals). This self-policing mechanism can (and should, imo) be extended/fortified with a "peer evaluation" portion of the project. But by doing so, the scenario becomes more capitalistic since each member's grade would (at least somewhat) reflect their effort. So let's forget about that aspect for the moment (although it's worth noting that the scenario is optimized by introducing capitalism).
SO. Our analogy began to break down as soon as we observed the self-policing mechanism. Even without peer-eval: shirkers can't hide, and there is punishment for shirking (in the form of condemnation by peers and/or reprimand or worse from the instructor. More drastic measures are not often taken in a scenario with kids in a school group project). And yet I think we all still agree that some members end up taking advantage of others. These students are often among the "lowest performing." We can't avoid the effects of this. More and more of the "middle-performing" students who are a bit torn between their innate desire to be all that they can be and to be lazy will inevitably follow suit. There is an unavoidable snowball effect until even the highest-performing, most "magically" driven members are affected. They will either become disenchanted with the notion of putting forth maximum effort, or they will be inundated by the burden which now rests on only their shoulders. Group projects don't always illustrate all of these effects to a great degree since they are over and done in a month or so. The analogous scenario in our society lasts decades for any one individual, but is actually an ongoing process from one generation to the next.
NOW. This analogy began with a group of FIVE. And there exists a self-policing mechanism which is 99% absent in our society since we can easily conceal nearly All aspects of (legal) behavior (and even some illegal behavior, perhaps). So let's expand the group project to a size of 30 (and assume that the scale of the project is appropriate for that number of members). The elegant self-policing mechanism becomes exponentially less efficient and less effective. Speaking to one person directly is still a viable option, but as we know this strategy is a 50-50 at best. It often ends up being one person's opinion vs another's. Gathering the entire group to address concerns of just one member is very difficult and very inefficient. Increase the size to 300 and it's impossible. A small sub-group could be rallied, but there is no way to ensure that this group will be an unbiased "simple random sample" representative of the entire group. In fact, it is likely that it will be the exact opposite. Sarah will likely form of group from her friends to maximize her chances of achieving her desired result. What about going to the instructor? That would still work with only 30, perhaps. Although it seems silly to demand the instructor's full attention for every little issue that pops up. If the group were 300 or even perhaps 60, the instructor could no longer keep up. More instructors? Sure, but if the instructor is (correctly) analogous to our government, the ratios we are hinting at are certainly not realistic/sustainable. Our political leaders have thousands and millions of constituents--not dozens haha.
The previous elegant, efficient, and effective system has gone to complete shit. Even worse, the beneficial (and capitalistic) concept of a peer-eval is no longer feasible. Each student clearly cannot be expected to evaluate every other student. Small groups could be randomly made by the instructor, but there still does not exist an analog to this in our society since we do not have access to other members' details. To make socialism even have a prayer of working, we would need to institute a policy of full disclosure, which would clearly work to reduce our freedom--the thing we hold most dear and which socialism is already diametrically opposed to. Even in such a scenario, the only incentive would be FEAR of condemnation by society. This is Complete Shit for motivation. A system like this will eventually result in a minimization of a society to the point of its destruction, with the only exception being a small, surviving group of the ruling elite (think: Rothschild).
Conclusion: socialism is a necessary and beautiful thing. It is the underpinning of our civilization. However, when expanded beyond a Very small scale, it has myriad negative effects. The goal of socialism is to end up with a more level playing field. Its supporters are shortsighted though, because they do not consider that this "level playing field" will continuously seek an overall lower level, further distancing society from a small group of ruling elite, and only making it easier for said elite to maintain control and ensure the continuation of its power until the actual source of its power is completely destroyed. Even the elite are mistaken in their (admittedly diabolical) benefit of socialism, because without a large society to extract from, their power (money) is meaningless. Hopefully they keep their skills sharp
Every time that one person helps another with no expectation of direct, tangible reward, it is socialistic. The value of this type of thinking cannot possibly be overstated. But when the concept is expanded and made systematic, free will is lost. Freedom is lost. And in the absence of an appropriate dose of capitalism, incentive is absent.
Socialistic scenarios are fabulous, but only in their naturally-existing small scale. When they are (designedly) expanded beyond a Very small scale, shit hits the proverbial fan. All of this reasoning is based on a very basic understanding of human nature, which, if not already possessed, can be easily obtained by thoughtful observation of one's daily interactions combined with honest introspection.
There is just one last thing to say, which ties all of the above to the actual topic of national education. If anyone has actually read all of the above or at least scanned it for accuracy, please let me know if you'd like to hear the punchline.