Fuel and food are excluded from core inflation not because they're unimportant (they are in fact incredibly important) but because they are much more volatile in price--going up and down in bigger increments--so that you get a more stable view of inflation by excluding them.
But it's a bit of a nasty trick because food, in particular, has inflated in price a lot the past 3 years. Some items, like sugar, are legitimately double the price they were.