> Why those arbitrary thresholds?

The broad idea is you want a number low enough that people don't price inflation expectations into day-to-day pricing but not so low that a hiccup causes deflation.

The empirical evidence around inflation persistence is a bit all over the place, but broadly suggests people start daily indexing between 2 and 5%. When that starts to happen, restraining inflation without causing a depression becomes incredibly hard, because people will actively countermand policy moves.