Why is a higher inflation rate bad for international competitiveness? Why if there's a higher inflation rate in country A then its exports are less competitive and its trading partners prefer to buy from countries with lower inflation rates?
Competitiveness simply means how expensive goods of a country are when compared. To correctly compare we would need to transform everything into a(ny) single currency. To do this correctly we need two elements: a) the actual price of the good and b) its exchange rate. If a country has higher inflation, then nominal prices increase, the goods are more expensive, less desirable and therefore due to (a) competitiveness decreases.

However over time purchasing power partiy (called PPP) holds. If it holds (typically does in the long run) then due to higher inflation in a country, the currency will likely lose value (depreciate) and competitiveness will increase due to (b), in which case it will eventually cancel the aforementioned effect (a) in which case your confusion is completely justified, there should be no effect.

However since PPP does not always hold and especially not immediately, higher inflation reduces competitiveness.