I have a few comments and criticisms to tender about this post.

1: Your table of systems of governments and their attitudes has a couple of problems.

• Communists, even the Vanguardist Marxist-Leninists of the USSR, would not agree with your characterisation of communism as "big government". A core tenet of Marxism is the "withering away of the state". They maintain that, once workers obtain free and equal association, there will be no need for governing bodies or legal frameworks. I think this is utopian, but at the very least, the end goal of communism is a stateless society, where production lines are administrated democratically. (It follows that communism would also be against state capitalism.)

• Libertarianism has left-wing and right-wing variants. This table only describes right-liberarianism. If right-libertarianism is adjacent to anarcho-capitalism, then left-libertarianism is adjacent to anarcho-syndicalism, and is immensely important in any account of government systems (it is the original form of libertarianism, after all).

2: Your criticism of the last two memes overlooks their main thrust. Critics of right-libertarianism argue that very strong property rights result in the accumulation of political and industrial capital by property owners. A land owner has a greater opportunity for wealth (rent streams, production lines, etc) than someone who doesn't own land. This additional wealth permits the acquisition of more land, which generates more wealth. Small inequalities grow to larger inequalities as land owners use their increased bargaining power to become bigger land owners, while people who don't own land are forced to commodify their labour.

You might argue that the difference between a land owner and a non-land-owner is the former initially obtained land by hard work, while the latter was lazy and unproductive. Your left-libertarian interlocutor would interject and say "Even if this is true, it is only true in the beginning. As generations give way to the next, the primary means of acquiring land is inheritance, not hard work".

tl;dr version

1. Your table incorrectly describes communism, and leaves out important schools of socialism that emphasise decentralisation and liberty.

2. The memes in question rest on the socialist assumption that land and capital will naturally accumulate into the hands of a small number of people. These people will be immensely powerful, and can subjugate everyone else. You do not really address this assumption.