it's not... it's competing in the market for profits. citadel makes plenty of money from trading, separate from fee-based business

There are markets that pay people to trade to provide liquidity.

that seems like an over simplification. however I do have an aversion to "MBA types" skimming over complicated concepts with the blanket "nerdy mathematics" techniques.

Market making itself is a market, and people compete on cost and speed

I’m pretty sure Citadel securities makes more money from their non-wholesale businesses (I.e. on-exchange trading) instead of their retail pfof business. Either way, they are very successful in the competitive hft/trading arm as well as retail.

The hedge fund quant arm is also extremely successful.

I agree with this, but the comment I replied to is responding to an article about market-making.

Citadels’s market-making arm, Citadel Securities, IS extremely competitive in on-exchange trading. They don’t just do wholesale market making (I.e. service for a price), they provide liquidity on-exchange as well (much more competitive/latency/alpha based than service-at-a-price). They’re also very good at the hft taking.

Given, within Citsec, the retail market making arm is fairly segregated for compliance reasons, but it’s far from the only market making activities they engage in.

In reality there isn't a distinction between "market-making" and what you would consider "beating the market". Market makers employ the same models and approaches as those who "beat the market", because market makers need to know when and where to quote in order to maximize profitability. And people who classify themselves as those that try to "beat the market" also provide liquidity, making them de facto market makers, even if they often take liquidity too. So, people in the industry don't attempt to draw a clear line between the two categories, because they are so overlapping in practice.