In old times, trade happened through barter — goods exchanged directly for goods

Why

Riya's respect for the old system is understandable — barter genuinely did let people trade for a very long time, so it clearly worked to some real degree. The catch is a specific, well-known problem called the 'double coincidence of wants': for a direct swap to happen, YOU must have exactly what the OTHER person wants, and they must have exactly what YOU want, at the same time. A farmer with extra wheat who needs shoes has to find a shoemaker who happens to want wheat right now — if the shoemaker wants rice instead, no trade happens at all, however much wheat the farmer has. Money solved exactly this: a shoemaker will accept money for shoes because they know THAT money can later buy them whatever they actually need, breaking the requirement that both sides' wants must match perfectly at once. Test: imagine trying to 'pay' a doctor today with a sack of onions — the doctor would have to somehow want onions specifically, right then, or the exchange fails, which is exactly the daily problem barter created. Her brother is right: barter needed both sides to want exactly what the other had at the same time, and that difficulty is precisely what money was invented to remove.