I'm not an economist, but I suppose that yes, in a sense it's true. An economy requires the value of money to be stable or very slowly decreasing in time. To obtain this, the amount of money in circulation must roughly match the amount of wealth. Since wealth is usually increasing, so has to be the total amount of money for its value to remain stable.
If you want an economy that encourages investment and trade then you want people to have some inherent motivation to spend money rather than hold on to it. The easiest way to do this is by introducing small amounts of inflation. At the very least we know that more people are being produced in the world, and people desire money, so merely by the practice of reproduction we are creating more demand for the same amount of money over time.
It's a nice story, but it's unconvincing. I would agree that a fixed supply of money might become more valuable as human population increases.
But I'm utterly unconvinced that 'prices can only increase' for the economy to work. For example, in electronics prices for hardware have generally fallen in nominal and real terms and yet it's still a pretty big industry.
"Nice story": it's not like I'm making up stories to convince people.
Think of a house: would you buy one if you knew that just by waiting a year its price would be 80% of what it is now? And the year after 65%? You'd probably just wait. If you waited long enough, you could buy one for, literally, today's peanuts.
Electronics sounds like a good counterexample, but electronics are also developing at extremely high speed. The price of a given device decreases very rapidly in time, but new more powerful devices come on the market every day. Sure, you could have waited five years to buy an iPhone 1, but that piece of electronics is now almost worthless compared to the other options you have on the market.
