This statement isn't true, and here's why:

Let's pretend that the Peercoin universe consists of two people. In reality, many more people than that hold Peercoins, but for the purposes of this analogy it will be much simpler.

Let's also pretend there are only 1000 Peercoins in the world (we could do this exercise with the actual monetary supply of 20.752M, but would create much less pleasant numbers to work with.)

Person A holds 900 Peercoins.

Person B holds 100 Peercoins.

In this scenario, both Persons are rational supporters of the Peercoin network, and wish to maximize their coin supply, and choose to use Proof-of-Stake minting.

Over the course of one year, both will increase their holdings by 1%.

Person A now holds 909 Peercoins.

Person B holds 101 Peercoins.

At this point in the argument (as some other crypto supporters will mention), it is clear that Person A has been unreasonably rewarded. Person A has gained 9 Peercoins while Person B has only gained 1 Peercoin, and so the *rich have become richer*.

Right?

Well, it turns out that it's not at all true. In the first scenario Person A has exactly 90% of Peercoins in existence (900/1000) and Person B has 10% of Peercoins in existence (100/1000).

In the second scenario, Person A has exactly 90% of Peercoins in existence (909/1010), and Person B has exactly 10% of Peercoins in existence (101/1010).

The total share of their investment in Peercoin from an enterprise level has not changed.

If the market capitalization of Peercoin didn't change (let's say that the total market capitalization stayed at $10M), neither Person has gained more value than the other. Each Person gained 1% in coins, and had their coins de-valued by 1%. Person A would still have $9M worth of coins and Person B would have $1M worth of coins.

The other scenario that might have occurred is that Peercoin's market capitalization increased. Let's say that PPC did well and the market capitalization increased from $10M to $20M.

In this case, Person A made much more money. His coins went from being worth $9M to $18M, while Person B's coins went from being worth $1M to $2M.

Can anyone legitimately argue that Person B deserved to have the same real-world fiat gain as Person A, even though Person A took 9x the risk in investing in Peercoin?

And that is why "the rich get richer" is a basic error in understanding of Peercoin's Proof-of-Stake mechanism.