There exists many values of X where borrowing money from X constitutes printing money. For example, when you borrow money from a bank, the bank prints money. It credits your account with new money, it does not transfer money into your account from another account.
It's fairly straightforward to prove that increasing the size of the government deficit = printing money.
1. The first step is that the government prints debt (a Treasury instrument, for example). I think we would agree on this.
2. The government then needs to monetize the debt... essentially swapping the new debt with reserves held by some bond buyer. There is no shortage of reserves (this is certainly true today. But even when there were reserve requirements, or in the time before 2008, there was still practically no shortage of reserves. I can provide a separate explanation for this). You may stop and say "but what if there is no bond buyer?" or "but what if there are bond vigilantes?" US banks will always swap excess USD reserves (where excess means beyond what is necessary for settlement) for USD treasury instruments because the latter pays higher interest.
3. The government now spends its reserves, transferring from the US Treasury to a private bank upon making purchases. This becomes new bank credit, aka freshly printed money. In other words, a private bank receives reserves via the Fed's payment system and must credit the recipient's private checking account with new money.
4. The reserves that were considered "excess reserves" in step 2 are now back in the banking system, ready to be swapped again for new debt instruments.
In other words, the net impact on private bank balance sheets is, just from fiscal spending (no activity from the Fed other than as a payment/settlement system):
- The assets side gains a treasury instrument
- The liabilities side is credited with new money caused by purchases by the US Treasury. This is spendable US dollars.
- No change is seen in the quantity of bank reserves