The value of a currency is the trust people have in it, that the dollar, pound, franc, whatever you earned today will buy what you need tomorrow.
If you monkey with the currency for short term political gain, that trust is eroded. Sure someone may benefit from the meddling this time, but that person knows full well that if the rules are fluid they might be the one who suffers next time. It doesn't matter if the central banks put rates up or down; every change will reduce the currency's value. The way to restore value is to build confidence back up and the way to do that is to resist the urge to meddle.
Why should they not adjust the interest rates? If they state clearly that they want to fight inflation - nobody will be surprised and no trust will be lost.
Because there ain't no such thing as a free lunch. All you can do by changing interest rates is shift the benefit and the pain from some people to some other people - and back again the next time you tweak it.
So? Fixing inflation is at least as good a goal as fixing interest rates.
(It is probably better.)
Your argument reversed:
"All you can do by [letting rates of inflation change] is shift the benefit and the pain from some people to some other people - and back again the next time you tweak it."
Well, that's not quite true. If interest rates change only rarely, then you can plan. "If I save I will get this much interest", "if I get a mortgage, it will cost this much" and so on. There's value in that predictability. Once you take that away you force people to hedge their bets against uncertaintly and that increases the cost of every transaction. This manifests itself as "economic slowdown", e.g. "I won't do this thing I planned, because I need to put some aside in case my costs go up".
If you fix interest rates - you can make very good nominal predictions. But nobody knows how much those x dollars are really worth when inflation is allowed to float.
Also I should point out that inflation is not a natural phenomenon - it is the direct result of deficit spending by governments. Think of it as sucking money from the future into the present before the value underlying that money is created. Again, deficit spending is done for short-term political gain.
For example the oil-rich states of the middle east see a lot of inflation right now. Expensive oil brought more new money than more new goods had been provided in the short term.
If you monkey with the currency for short term political gain, that trust is eroded. Sure someone may benefit from the meddling this time, but that person knows full well that if the rules are fluid they might be the one who suffers next time. It doesn't matter if the central banks put rates up or down; every change will reduce the currency's value. The way to restore value is to build confidence back up and the way to do that is to resist the urge to meddle.
None of this is rocket science.