Think of it more like a system of reactions that feed off each other: wage increases, pro-active price increases by retailers, etc.
It doesn’t necessarily matter what started accelerating inflation, but it is important to stop the system from gaining too much momentum and slow it down if it does.
Lowering employment and slowing spending with monetary policy are the best tools we currently have to do this.
Of course, the Federal Government could also rein in the outrageous deficit spending, which would help greatly but this is too politically difficult.