In an ideal world the inflation rate is 0%, but our control lags considerably so we will weave around the objective. We want to minimize the harm caused by this weaving--and going below 0% causes more harm than going above it does. Thus we deliberately aim far enough above 0% that the normal variation won't cause it to dip below 0%.
Fear of deflation is only one reason that central banks target a small positive inflation rate.
(1) inflation makes it possible to set negative real interest rates. When inflation is very low, the only way that central banks can provide the stimulus of negative real rates is to make nominal rates
negative.
(2) companies can give real pay cuts to poorly performing employees. (it is much easier for companies to leave a nominal wage unchanged than to lower it.)
(3) some sectors, e.g. restaurants, may be stimulated by lower real prices. (it is inconvenient or costly to reprint menus for a small inflation.)
Central bankers would like to see inflation
above the nominal 2% target (although they don't say so publicly), and would then be happy to see higher, more normal, interest rates. Indeed, a
hope from stimulus is that it will lead to higher employment and an associated modest boost in inflation.