"Order flow toxicity is the measure of a trader's exposure to the risk that counterparties possess private information or other informational advantages."

Usually, flow from other MMs isn't toxic.

Toxic flow can also just be someone who's executing a very large order, even if that counterparty isn't informed. If you fill them as they are starting to work their order, you could get run over as they continue to finish that order and push the price against you.

Flow from other HFT / market makers is often very toxic. They are playing the exact the game as you.

Right, sure, and that game is not lifting the market, generally speaking.

Other market makers are often moving away from something they've seen but you haven't yet. When whatever that is hits you, the fills you got from the other market maker will look really bad.

Sure, but those short-term active strategies have little impact next to what big paper will lift in major macro markets.

Not sure exactly what you're trying to say but let me tell you, fills from other HFT firms are highly toxic.

Not aware of a market maker that also doesn't take liquidity as well. In fact, it probably would impossible to market make without also taking (you wouldn't be able to provide liquidity if your quotes were in cross with the market).

That said market makers do a lot more making than taking.

Usually too smart, on rare occasion they cheat. MMs inherently deal with information assymetry and adverse selection because they generally stand ready providing liquidity with quotes out in the world (though obviously width matters). Toxic counterparties are parties who decide to trade against you who have a better idea about “true” price than you. They might make or they might not, depends if the degree in which they’re right overcomes the spread they crossed. Other MMs can be (and often are) toxic.

or doing latency arbitrage

that falls into the category of knowing the “true” price better than you do