It’s hard to fit the two main economic arguments about the effects of monetary inflation into pithy political statements. But, to say, as your friend implies, that monetary inflation doesn’t matter because all prices and wages go up together is mistaken.
Monetary inflation will push the prices of some goods up further than the prices of other goods and it will push the prices of some goods up sooner than the prices of other goods. Because of this, income is redistributed away from those who are selling goods whose prices go up later and not so much and buying goods whose prices go up sooner and further. Income is redistributed toward those who are selling goods whose prices go up sooner and further and buy goods whose prices are going up later and not so much. These changes in the structure of prices change the profitability of lines of production and therefore, entrepreneurs shift resources toward the more profitable and away from the less profitable lines.
Monetary inflation, therefore, retards the efficiency with which entrepreneurs arrange production to satisfy people’s consumption demands. Instead, resources are forced into production to serve the interests of the state.
Take a look at the lectures on money and monetary policy for more details.