Good question and I don't want to worm out of it but it could be four or more things.

1. I'm wrong
2. The other user is wrong.
3. The other user and/or I distinguished between falsifiability and Popper's falsifiability, which means we could be talking about different things and so both be right (or both be wrong) at the same time.
4. The other user and I are in agreement but we expressed our points in different ways.

Popper's argument was that scientific progress rests on deduction. Specifically, he proposed a hypothetico-deductive methodology. Essentially, the scientist begins with a hypothesis and tries to disprove it. Whatever the result, they next create a more accurate hypothesis and try to disprove it. And so on.

In this set up, a few points follow. The hypothesis must be falsifiable. The method of reasoning must be deductive. This assumes a model of deductive knowledge. (Or deductive 'epistemology', which refers to a theory of knowledge—Popper's was anti-Marxist, anti-working class.) There isn't much if any room for inductive or abductive reasoning, here.

There is no room in this for dialectical materialist epistemology (Marxist theory of knowledge). I'm not qualified enough to say much about the relationship between dialectical materialism and deductive, inductive, and abductive reasoning. I'm only saying that Popper insisted on deductive reasoning, to the exclusion of inductive, abductive, and dialectical materialist (regardless of any overlap/relationship between the latter).

Falsifiability at is most basic simply means that something can be disproved. Popper argues that scientific knowledge cannot be proved true. To him, we can only becoming increasingly confident that something is 'not incorrect'. The more times that a theory is not disproved, the more confident we can be in relying on the hypothesis.

He got to this point by criticising historicism. The idea that if something has happened in the past, it is a reliable indicator that it will happen again. This is the kind of reasoning on which e.g. astrology is based. It's faulty. Popper equated historical materialism with historicism to discredit the scientific basis of Marxism.

This is why Popper insists that knowledge accumulates not by proving lots of facts/theories but by failing to disprove facts/theories. Ultimately, he was trying to find a way to stop people from looking at the past to predict the future. Popper's version of falsifiability implies that as we cannot falsify past events, they have little to no role in science.

E.g. it's not possible to conduct an experiment to disprove that conditions in nineteenth century France would always lead to the Paris Commune. There are too many variables. A critic could always say, yes but if Pierre Secondname didn't do XYZ, the whole thing would have been different. The hypothesis cannot be put in falsifiable terms, so it has little to no scientific value.

This summary should make it clear that for Popper, scientific knowledge can only advance in tiny, tiny, steps, because there is little room for variables. There can be no scientific theory that includes variables that make it difficult/impossible to disprove the central thesis. (See the Michael Patenti bot text in the auto reply to see how the bourgeois ignore Popper when it suits them.)

But Marxism is scientific. Just not in the way that Popper narrowly defines science. If a Marxist theory, etc, is falsified, disproved, etc, the claim must be abandoned.

The difference is that Marxists aren't starting with the hypothetico-deductive methodology. They start (and end) with dialectical materialism: Marxists analyse the process of change within contradictory internal relations. Then they make predictions. If the prediction/theory/analysis is shown to be nonsense, it is falsified and we need to take another look.

Marxists are working with a very different set of epistemological assumptions to Popper, meaning the way that we decide whether something is falsified is different.

Popper's falsifiability implies we must abandon the Marxist project because it's impossible to disprove the theory of revolution (that capitalism will lead to communism by virtue of its own contradictions). That is, we cannot unequivocally say that revolution is inevitable. It might not happen or it might take another 300 years.

Piketty makes a similar, bizarre comment at the start of Capital in the Twenty-First Century. Something like, Marx was wrong because he said there would be a revolution and we haven't had it yet (in the west, but I won't focus on the chauvinism, here). Key word: yet. We could prove revolution is possible when one happens, but Popper says that proof isn't enough for a scientific theory.

To say that revolution hasn't happened yet wouldn't convince Popper that it's a scientific prediction. He would say that if you can emphasise the 'yet', the theory isn't falsifiable because there is no way for him to disprove it (within a single human lifetime). Unless it happened, but then we're back to square one, with trying to prove a theory to be true rather than trying to disprove it.

Historical materialism (which is dialectical materialism applied to human social relations) is not the same kind of science as the type that's involved in putting a plane in the air, treating an infection, or growing crops. Different types of science require different concepts and standards of falsifiability.

Popper says there's only one standard, and his standard is an anti-Marxist one. Popper was a mere scribe for the bourgeois world outlook. So he's not the source of so many problems. But that outlook is the source of so many problems. E.g. treating (neo)liberal economics as a science until someone points out it's non-falsifiability, at which point it becomes, 'Well your sociology and "social sciences" aren't science either, so there' and they pull a face at the worker wondering why they're poor.

As Maurice Cornforth opens in Dialectical Materialism vol 1, all theory, all science, is class theory, class science. Popper pretends, like a good little liberal, that his is universal. That doesn't mean we throw away all bourgeois scientific concepts, such as falsifiability. It means we need to proletarianise them.

If a theory is falsified and shown to not help liberate the working class, it must be abandoned. Brutally and swiftly. Incidentally, that's why I'm a Marxist-Leninist and not a left-com, anarchist, Trotskyist, etc, etc. Marxism-Leninism is the path taken by the Marxists who have been consistently proved correct (not falsified) or who have been wrong but abandoned their erroneous theory along the way. (Which also explains why MLs should take Juche and some other 'unorthodox' ideas seriously, but I digress.)

(Happy for a better scientist to spot any flaws in my explanation!)

I feel like you shouldn't conflate Popper (the man himself) and falsificationism.

Marxism is completely falsifiable.

I'm not sure about that. Look up theory-ladenness of observation, or see modulus' and my response for an ahistorical critique of falsificationism. Nowadays falsificationism isn't that well regarded anymore. Regardless, Marxism can still be considered scientific. There are better metrics to demarcate between science and pseudoscience than falsificationism. I don't like how (at least in the West) they still teach flavours of this shit in school (including hypothesis testing).

On Popper (the man himself), he was motivated in his work to introduce chauvinist and conservative ideas to gatekeep economic and social science from being considered a "science", both from his anti-communist beliefs but also because the logical positivists were too easy to dunk on.