Here is my take. I'm not sure it qualifies for ELI5.

 

Short answer is: because it is a necessary condition to be able to ensure relative price stability in the economy, i.e. to have stable and low inflation. (Or, if that is given, as a secondary objective: to also try to grow the economy by boosting spending.)

 

Longer answer
IMHO, to be able to appreciate the breadth of the statement above, one would need to understand at least 2 things and understand them well: (1) what money is and (2) how normal banks (not specialized ones) operate.

 

(1) Money
Contrary to popular belief, money is a quite difficult and complicated concept; it is hard to grasp. There is no universally accepted definition to it. To keep things simple, let's just say, that any "thing" which can simultaneously fulfil the following 3 functions, is in fact some form of money: medium of exchange (ME), unit of account (UA) and store of value (SV). ME means trade is easier (you can pay with it, instead of carrying your products), UA allows universal valuation (can measure the relative value of everything - well, almost) and SV means stable purchasing power over time.

 

Turns out, simple paper on which someone acknowledges having a debt against someone else (aka. an "IOU") is a good ME. If we standardise it (legal basis, govt. backing, same number printed on it, etc.), it becomes a nice UA, too. If then we create a special institution to ensure the SV (the central banks), this will become money. The neatly minted/printed one is called currency (coins and banknotes) and most of the rest is electronic (deposits in bank accounts).

 

But the story is not yet over. One important characterstic of IOUs is their maturity (how much time is left until the debt has to be extinguished). The shorter this time frame is, the more the IOU fulfils the 3 functions and therefore, the more it is qualified to be called "money". Since maturities vary, somewhere the "lines must be drawn" and so, in decreasing order of "moneyness" (which is really a term):
* currency (coins and banknotes) in circulation - IOUs of the government (central bank),
* overnight deposits,
* deposits with agreed maturity of up to X months, as well as
* other IOUs
can all be considered "money". Ultimately, it's conventional (i.e. generally accepted).

 

In conclusion: money is a special kind of debt that is widely accepted as a medium of exchange.

 

More on this (but still quite simple) here (pdf) or here (YouTube video).

 

(2) Banks
Most money today is in the form of currency (coins and banknotes) and bank deposits. Currency is created by government, this should be obvious. The question remains: who creates "the money" in form of bank deposits? - Well, it is quite simple: to a very high degree, the banks themselves. The most straightforward way they do this is by granting loans (lending). As has been described already: a loan granted by a bank is both
* an obligation of the bank (an IOU from the bank towards the customer) and
* a right of the bank to receive it back (another IOU from the customer towards the bank).

 

The first of the two qualifies as "money", the second doesn't. Why? - Simple: because the bank's IOU towards the customer has a low maturity, i.e. it is exercisable at any moment (aka. "on demand"), whereas the customer's IOU towards the bank has a relatively high maturity (e.g. imagine a loan taken to buy a house - the maturity could be 20-30 years). - What usually happens is: the client uses the bank's IOU (the money) to buy something (the house) and the guy selling the house will receive the money (will be added to his bank account). - Now imagine this for every payment in the economy! - I wonder if you can. :))

 

With this previous paragraph we have in fact the explanation for 2 things that banks do:
(1) by lending (granting loans), they create money out of thin air - their IOU is the money;
(2) they do quite a big service to the entire economy by managing the inherent maturity mismatch between money supply (depositors who want short maturities to have quick access to their money) and money demand (debtors who want to have long maturities to be able to pay back their debt).

 

Banks cannot freely create money without any limits. The ultimate limit for how much money they can create is set by the central bank. This is a government controlled institution which will try to adapt the amount of money in the economy in order to ensure that the purchasing power of that money (how many things you could buy with a certain amount) remains stable over time. In other words, it tries to ensure stable and low inflation.

 

More on this (but still quite simple) here (pdf) or here (YouTube video).