What flaws do you see in my argumentation?
There are several flaws in your thesis.
First, I know USSR and eastern block are commonly labeled 'communist countries', but they were not communist technically speaking so you cannot really use them as an example of failure of communism. USSR and eastern block were by definition socialist country (it was even in the name Union of Socialist Republics, Czechoslovak Socialist Republic etc.). These countries had an official stated goal to become communist in future, but none of them did. Hence if you want to discuss flaws of USSR and eastern block you should focus on socialism, which is the system they had.
This is not just nitpicking terms. A country is a socialist country (at least economically) when majority of means of production is communally owned, either by state or through coops (Nove 2017). Communism was supposed to be the final stage of revolution after socialism, when state would 'die out' and society would be completely stateless, moneyless and classless. You can criticize both systems but there are clearly huge differences between them so it is important to be clear what you are talking about. For example, in communism (as defined by let's say Marx) there is no state to redistribute resources anymore so your critique would not apply.
Second, you are right that most people derive utility primarily from their own or their close relatives and friends consumption, so when their income, which enables consumption of goods or leisure, is not tied to their own performance but collective performance, they will not have the incentives to provide optimal level of work effort. However, you seem to focus on this point too much, as if it would be the main or full explanation for economic failures of socialism.
This point alone is not really sufficient, because you can, and many socialist country did, replace market incentives with incentives based on threats of violence, and that can motivate people to work too. You can even argue that threat to be sent to a gulag is similar motivator to efficiency wages under capitalism (e.g. see Miller & Smith 2015). You can criticize this on moral grounds but it is certainly a way how to provide strong incentives to work. You could even argue that threat of having you and your family sent to gulag is greater incentive to work than simply getting resources proportional to your effort as in market system. So this alone simply cannot explain failure of socialism.
The critique you got was also flawed because they do not pertain to either communism or socialism. Rawlsian Max-Min tax design that taxes rich to redistribute to poor is neither communist, nor socialist. Under socialism primary tool of redistribution was forcing everyone who was able-bodied to work and state simply set wages and/or imposed restrictions on how much output person can get. Under communism there isn't even state to set wages or to tax people so using that as a defence for communism is absurd.
How would you explain it?
This is not my personal explanation, but the general explanation in literature. The two major systemic flaws of socialism are as follows;
- Economic Calculation Problem
Socialism, with a small exception of market socialism (which would be organized around private coops rather than state ownership), necessarily has to rely on central planning due to state ownership means of production. In turn centrally planed economies lack price mechanism that is necessary for economic calculation and that provides people with incentives to be economical.
Prices in market economy provide both information about relative scarcity of goods, services or factors of production, as well as incentives to act on that information. For example, if you have an economic problem like should I expand pin production in factory A or B you can solve it by looking at prices (e.g. in which location price of pin is highest, where the price of capital and labor is lowest etc). This means that the production is expanded when the pins are dearest and where the capital and labor is less scarce, and factory owner has incentives to get it right by earning more profit if they act on these prices. However, centrally planned system does not have such mechanism and thus simple economic problems such as should I expand production line in pin factory A or pin factory B becomes unmanageable. Even if market incentives can be replaced by threat of violence, it becomes extremely difficult if not impossible to judge relative scarcity of pins, labor and capital when there are no genuine market prices. You can't simply poll people as stated preferences generally do not correspond to true revealed preference. Capital and effective labor are extremely difficult to measure so you can't easily know their relative scarcity just by counting machines (since different machines contain different amounts of capital and different people different amounts of 'effective labor').
If you wan't to learn more about this issue you can read Hayek's essays (1935) and (1945), the latter on market mechanism was even what earned him Nobel Prize in economics, so this point is widely accepted in profession.
- Common Ownership & Other Bad Institutions
Core economic characteristic of socialist economies such as common ownership of all factors of production itself is economically inefficient. In economics, it is accepted that countries with good 'inclusive' institutions, such as strong property rights, are more productive and able to develop faster (or even develop at all) than countries with bad 'extractive' institutions, such as forced labor (see Acemoglu 2008, Acemoglu & Robinson 2000a, 2000b, 2001, 2006, 2008; Olson 1984, Bates 1981, 1983, 1989 and sources cited therein)
Strong property rights, free access to labor markets, free enterprise are all examples of very important inclusive institutions that help economies to prosper and grow. Some of these institutions are not compatible with socialist economies (e.g. free enterprise, strong property rights).
There are various reasons for this. For example, even in absence of the problem of economic calculation (e.g. under market socialism), common ownership of factory would not yield optimal levels investment into the factory, because workers are considered to be more risk averse than entrepreneurs (which is why they choose the security of wage as opposed to uncertainty of profit i.e. due to self selection). This is only one example, of problem of common ownership one could provide more, but this answer is already too long you can read the sources I gave you in previous paragraphs for more detailed discussion.
Free labor markets are important because there is fundamental informational asymmetry between you and state. You know best your own qualities and strengths and weaknesses and preferences. Moreover, people do not generally have incentive to reveal their true nature to state, especially not under centrally planned economy (e.g. if you are more productive but wages in an industry are fixed you would not reveal your productive nature to the state). Hence, it is nearly impossible for state that centrally plans economy to optimally utilize labor. Such informational asymmetries exist even in market economies between works and companies but in market system these can be solved through price mechanism (i.e. different wages linked to performance), or in some industries company using sole proprietors for some tasks (since the proprietor gets profit proportional to effort not fixed wage there is no reason to hide his type).
The above are just few examples. This is too broad topic to explore fully on Q&A site.