[Economics] Why does the inflation not follow the money supply?
Solution 1:
This is because classical economic theory absolutely does not say that:
inflation occurs when the money supply is increased faster than the economic growth.
Even in most basic 101 models inflation depends on variety of factors. Inflation is determined by changes in price level which in turn depends on what the money market equilibrium is. This is given by equation of exchange (See Mankiw Macroeconomics pp 87) as:
$$MV=PY \implies \ln P = \ln M + \ln V− \ln Y$$
Where M is the money supply, V velocity of money, P price level and Y output. In the log-linearized version the effects of right hand side variables can be interpreted as % changes.
Even in this most simplest model your statement "inflation occurs when the money supply is increased faster than the economic growth" would only hold if velocity of money would be constant but in real life it is not. As you can plainly see from the data provided by Fed the velocity of money dropped drastically since the 90s which offests most of the increase in money supply during that period.
Lastly, the model above is still just the most simplistic 101 textbook money market model. In more realistic and complex models there are more variables that matter. For example, inflation expectations are absolutely crucial. Inflation will not move drastically if inflation expectations are well anchored (e.g. see Castelnuovo et al 2004; Kose et al 2019 or Lejsgaard & Grothe 2014 and sources cited therein for more info on the concept).
In addition, as famously shown by Krugman (1998) what matters is not just the actual change in money supply or other quantities but what are peoples expectations about changes in money supply and so on. An increase of money supply that is not credible to be permanent and expected to be quickly reversed will have no effect on inflation as if it would never even happen. Furthermore, Krugman also showed that when nominal interest rates are at zero lower bound (ZLB) even large monetary expansion won't necessary be inflationary. The reason for that is that if you would want to go significantly below ZLB the peoples will strictly prefer to hold cash and any increase in money supply will be completely offset by drop in velocity of money.
There are also further nuances to this but full overview of modern scholarship on this topic would be well beyond scope of SE answer. I recommend you to have look at Monetary Theory and Policy by Walsh or Woodford Interest and Prices and sources cited therein for state of the art models and more information on the matter.
Solution 2:
The question, as I understand it, is about the reconcilliation of classical theory of inflation with empirical reality. Put in those terms, it's very interesting the concluding question:
"Does the money accumulate somewhere, if so where?"
The very possibility for money to accumulate somewhere is a serious problem for economics. In fact, it's attributed to M. Kalecki the claim that "economics is the science of confusing stocks and flows". The inability of handle with stocks or, put in other way, the need to balance flows, has puzzled mainstream economics long ago --neccessary balance of flows is, for example, the root of the so-called Say's law--.
Krugman --quoted in other answers to this question--, for example, has reckoned his inability to understand the role of money creation in the purchasing power creation (see here or here), due to the unability or lack of will to handle with stocks.
But the fact is, if you take into account the existence of stocks, for example of money, --as you do in the question-- the possibility of hoarding eliminates any difficulty considering more money supply not automatically meaning effective demand, nor the oppossite. Ashtoundingly simple.
You can read more on these issues googling for "stock-flow consistency".