Earlier quoted context omitted.
Strictly economic theoretical speaking, inflation wouldn't happen if the money isn't "new" money, but instead is fully reallocated money. A likely picture would be less money going into assets (where wealthy people money tends to end up) and more money going into consumables (where poor people money tends to end up). However the money pile should stay the same all else being equal.
Inflation is generally defined by the price increase of a basket of goods. If you relocate money from things outside that basket to things inside that basket then inflation can increase without the money pile getting bigger.
At heart, inflation is a mismatch between the real value of the economy and the currency placeholder used to represent that. This is why governments can (and need to) keep printing money as the economy grows.