They have to fight the battle at hand which is inflation, if they are too late to raising interest rates which is now baked into market expectations anyway well then inflation really kicks off. The US and UK are raising interest rates , if the euro doesn't follow well then its exchange rate will continue to fall exasperating inflation. The most important commodities like oil are priced in dollars therefore it is vitaly important that this exchange rate is stabilised in order to control inflationThe worst thing the ECB can do now is increase interest rates to control inflation and slow down the economy.
During the financial crash the ECB was years too late in reducing interest rates until they ditched Trichet, now they are too late in fighting the current problem which is inflation, Will we have to wait until Lagarde is also moved on to tackle it?