Its basically because its a pre-emptive policy with a variable and often complex time-lag(6-18 months). The RBA cannot afford to wait until inflation is within their target band of 2-3% as we would experience quite a severe recession. Like i think consumer confidence/sentiment is at recession levels with credit growth also very low or falling?. These are all indicators of like a slowing economy where basically consumers will spend/consume less (or save more) and firms will generally invest less due to the higher cost of borrowing hence significantly lowering AD = y = GDP = (C + I + (G-T) + (X-M)) and therefore eco growth. So if AD keeps falling you have a multiplied fall in national incomes (or GDP) so you can actually have a negative economic growth. Since the demand for labour is a derived demand for g+s you will also therefore have a sharp rise in U/E as firms will scale back their production and lay off staff to compensate for the fall in demand for g+s. In a market economy without an govt intervention you'd see an extremely sharp downturn and large rise in U/E. Therefore by cutting the cash rate now, they will be able to ensure that the slow down experienced isn't as severe and that you have moderate/low future growth which will slightly raise U/E, rather than a full blown recession(2 consequetive quarters of negative growth) which would lead to a sharp rise in cyclical U/E which can transpire into other forms etc. So basically by acting in pre-emptive(in order to factor in the time-lag of monetary policy) fashion they can cushion the slow down (hence the name of "counter cyclical") so there is a "soft landing" rather than having negative growth which can have dire consequences on the economy. So when you say inflation should be the most important objective you have to also remember that U/E is also a major objective. In terms of Inflation you will see underlying eventually fall back into the RBA's target band of 2-3% as lower inflationary expectations, a fall in AD and as productive investment into the economy's productive capacity comes more on stream (or the responsiveness of AS is increased). In terms demand pull the low consumption levels and investment levels will lower AD and therefore lead to a fall in prices as there is less demand aye. In terms of cost-push, U/E will rise due to slower growth which lowers consumption and will lead to a fall in wage demands hence lowering demand pull and cost-push inflation. So due to the signs the economy is slowing, the RBA believes inflation will fall in the future(and they are right) and due to the time-lag of monetary policy they must pre-emptively(i.e. now) by cutting rates to ensure that AD does not keep falling in the future to prevent a recession in the economy and basically balance the objectives it has.
Btw wrong_turn although theorethically a higher inflation rate can lead to a depreciation of the dollar, the majority of our export income is derived from primary commodities which have an inelastic demand and therefore are not affected by changes in our inflation rate etc. The main reason for the depreciation was the expected fall in the interest rate differential between AUS and the US with the US cash rate expected to rise in light of their 10% rate of inflation while the RBA was expected to cut rates so carry traders and speculators sell AU and buy the green back speculating a rise in the greenback. There was also speculation of a fall in commodity prices as world growth falls. Remember that like 95% of all exchange rate transactions are speculative short term transactions with trade only accounting for 1%. Such a large depreciation would unlikely be caused by merely a high domestic rate of inflation.
