Capitalism is a system of distribution of goods with a basis of private property and competitive markets. In the past it has been praised for high rate of innovation and low costs of goods compared to older systems such as feudalism and aristocracy where small states subservient to a crown owned and managed industry.

Cool. Now tell us why it's been condemned. You've only got half the definition there, and that doesn't count as an honest explanation.

(Also: capitalism may work like that in theory, but it's never been fully implemented in practice. Every so-called "capitalist" economy has the rich putting their thumb on the scale to make markets less competitive in their favor. The "economics 101" definition you give is so simplified that it's useless for describing any real world economy. But that's another rant.)

I appreciate the concrete definition but Marx disagrees with you on most points.

1. Capitalism is a system of distribution of goods vs capitalism is a historical mode of production of commodities.

• I agree with Marx. Since almost all goods are created for selling at a profit (commodities), not distributed according to human need, this demonstrates that capitalism is not a method of distribution, as it is a way of determining what commodities get created, and who gets them. Capitalism is not just driving/sailing/flying shit around. Defining capitalism in this way is confusing because capitalism clearly isn't a method of distribution that relies on competitive markets, as much as it is a system of competitive markets that relies on methods of distribution.
• in fact Marx described capitalism as "anarchy in distribution" which explains why so many capitalists and supporters of capitalism are also anarchists.

2. Basis of private property vs basis of class antagonism

• I agree with Marx, but I don't disagree as starkly as the first point. More like Marx's criticism includes the private property question. Marx has no issue with individual ownership. However, Marx defines the "central contradiction of Capitalism" to be "socialized production, privatized realization of profit" which means that many individuals work together to produce what could only be produced collectively and with a degree of mechanized, industry (a distinct advancement of Capitalism over previous historical Modes of Production.)
• Basically, workers are paid a wage for our time, but capitalists are able to reinvest the value created in the production process to realize compounding returns.
• Private property -- when viewed in light of the antagonism between the capitalists who own property, and the workers who only own our time and are forced, or at least compelled, to sell it to the capitalists -- is not the abstract idea of "owning" something, but a system for deciding who gets to own what, and why. The system for determining this is based on "who can afford it" which unfairly benefits whoever has the money and organization, over poor, struggling, precarious workers.
• you seem to be of the opinion that government regulation as the bulwark against capitalist over reach is a given for a rational society, a very progressive perspective. But I think this view is a little idealist at best, and ultimately one that depoliticizes the the subject of how human rights were won in the first place. I think it depends on a very special kind of logic working perfectly in order to be true, examples of European social democracies are always good examples in the positive, but when other countries have tried to socialize parts of their economy, particularly land redistribution, natural resources, finance, oil production, etc., they might be invaded or have their governments overthrown in western capitalist funded and supported "color revolutions."
• The Marxist analysis of state power, is that the state is the manager of class antagonisms within the nation. So implementing government regulations to put controls on industry is a sign of democratic worker control of state power, aka, strong unions.

3. Your blurry conception of history vs Historical Materialism

• I think you're really flattening a lot of time, into a few sentences which def wins out on brevity, look at my effort-posting ffs, but confuses so much history. For example, does industry include the corvee system? So are you saying crown-directed production? Industrializing production was something the bourgeois capitalists did, from let's say, the early to mid 1600s in England, and then unevenly and to different degrees for the next 300 years throughout EU, and to different degrees in USA and in colonies. Industrializing production is, according to historical materialism, one of the means by which the then-ascendent bourgeois capitalist class seized actual power from the monarchies, and were able to win political power from the feudal monarchy, first in the form of parliaments and then constitutional monarchies.
• bourgeois capitalists defeated their monarchies and old ruling classes, and seized the colonial, patriarchal, cultural power along with state power. From there, each nation has developed as a result of the struggles between nations, and the struggles between the workers and the capitalists.
• exceptions are where peasants, workers, and revolutionary bourgeois overthrew colonially controlled states, also Russia and China are prominent exceptions that warrant their own histories separately and together, and in relation to the rest of the world. These are exceptions that are worth discussion vs your description of "2000 anarchists in Mexico" and various cloistered communities presumably all over the world not just in like Midwestern/Northeastern USA.
• In order to have real understanding of history, we have to be specific and not abstract in the way we approach any subject. In my experience, Marx is a much better way to figure out what is actually going on, than a way of making abstract ideas to suit this or that political view. People have used Marxism to twist history and politics into a view that benefits some elite, some new bourgeois. But that's not what Marx accomplished with his work, even if it is what future "revolutionaries" would accomplish with Marx's work.
• The reason this is possible, is that Marx's work was essentially practical, as is every aspect of our lives. Really understanding Marx is incredibly fulfilling, and not even that hard.

4. Creating or adopting abstractions and then debating their validity and universality vs "The philosophers have only interpreted the world in various ways, the point is to change it".

Nice argument, but you see I've already depicted you as the virgin Feuerbach and myself as the chad Marx in this meme /s

What's private property?