An economy produces two goods: apples and haircuts. The production function for apples shifts up or down every year at random, depending on the weather. The production function for haircuts never shifts. The weather causes relative prices to change. When there is good weather, and the apple harvest is large, the price of haircuts in terms of apples rises (the price of apples in terms of haircuts falls). When there is bad weather, and the apple harvest is small, the price of haircuts in terms of apples falls (the price of apples in terms of haircuts rises).
The central bank targets 2% inflation for apple prices. It ensures that apple prices rise fairly steadily at 2%, and lets the price of haircuts fluctuate with the weather. The central bank justifies its decision to target apple price inflation by noting that fluctuations in haircut price inflation are transitory and typically reverse themselves the following year. Apple price inflation gives a much better measure of the underlying long run trend of the inflation rate of the CPI basket, even though the CPI basket contains both apples and haircuts. Apple prices belong in core inflation; haircut prices should be excluded from core inflation.
If the central bank had instead targeted 2% inflation for haircut prices, it could have made the same argument for apple prices being excluded from core inflation.
It might be better to ask which particular measure of inflation correlates most closely with the unemployment rate, if you insist on targeting some measure of inflation.
Just one thought on reading Bank of Canada Deputy Governor Larry Schembri's presentation on core inflation.