Why should small open economies avoid interest rate policies? I've been taught that small economies open to capital flows should avoid manipulating interest rates because increasing interest rates will mean capital inflow which causes currency appreciation. Overall, interest rate policy causes exchange rate volatility. But why is the case for small economies? Why is the US or China less susceptible to this theoretical argument?
The trilemma or impossible trinity is said to be that it is impossible to have all three of the following at the same time:


a fixed foreign exchange rate
free capital movement (absence of capital controls)
an independent monetary policy


The United States prioritises the second and third, and only worries slightly about the first and its impact on trade.  Being an extremely large economy, capital inflows can only make a small difference to domestic market conditions, though during the world financial crisis some moments of fear did tend to push the relative price of the dollar up as international money sought a safe haven (abbreviated to risk-off sentiments). Currently it seems that the US can make moderate increases to interest rates in contrast to Europe or Japan, without a major impact on US exchange rates   

China prioritises the third and also the first in a managed exchange rate sense.  There are significant capital controls in China (more now than a few years ago), and they make it difficult for short-term capital flows to cross the border in either direction.  If somebody abroad wants to buy yuan-denominated shares or bonds, they will find it much easier in the rather peculiar markets in Hong Kong than in the domestic markets in Shanghai and the two often disconnect with significantly different prices for similar investments. This enables the Chinese government to pursue a domestic monetary policy without too many international concerns

A small open economy cannot follow the US example (being too small) or the Chinese example (being too open).  And in many cases smaller countries are more affected by international trade than similarly structured larger ones. So the exchange rate implications of changes in domestic monetary policy are more important to small open economies