For the Fed (can’t speak to Bank of England), it has in legislation what is frequently referred to as a “dual mandate” of “maximum employment, stable prices and moderate long-term interest rates.” [0] The 2% Fed target explicitly is justified as balancing stability and employment.

The ECB also has a 2% target, and its asymmetric explanation of stability may explain it: “By stable prices, we mean that prices should not go up (inflation) significantly, and an ongoing period of falling prices (deflation) should also be avoided.” [0]

Note that they define stability as avoiding signficant inflation and also avoiding significant periods of (even small) deflation.

[0] https://www.ecb.europa.eu/explainers/tell-me-more/html/stabl...

The bias towards inflation exists because it can reduce the real interest rate below 0%. Lowering interest rates below 0% is not practically possible. If we could hit negative interest rates deflation wouldn't be such a big deal.

If we could have negative interest rates, deflation would still happen, and people would still label it as a harbinger of bad economic times. Why? Because price deflation of a monetarily inflating currency is a symptom of an unhealthy economy. When the currency becomes a more attractive place to keep your money, it means the rest of the economy has become significantly less attractive - ie unhealthy. Deflation itself isn't what's a big deal, its the cause of deflation that is a big deal.

> The bias towards inflation exists because it can reduce the real interest rate below 0%

And why would we want such a thing? With real interest rates below 0, everyone could take a loan out, sit around and do nothing, and then collect money from the "lender" later.