Danish central bank pursues a a fixed exchange rate policy against euro. If they do so, why won't they just directly use euro instead? It seems that having such policy eliminates the main advantage of having an independent currency (stabilizing economy using monetary policies), yet it creates additional transaction costs (compared to using euro).
There are economic reasons for Denmark not to use the euro. Although, as a Dane, I must say most people voted against the euro to make a protest vote against "European elites", there are some economic reasons for not joining.
Flexibility. There are historic precedents for Exchange Rate Mechanism II rules being suspended in case of crisis. For example, in 2008/2009 because of the Great Recession countries were allowed to float their currency outside the bands temporally.
In 2000 nobody really knew how the euro will fare in the long term. Even today it is not clear if the euro can be viable in the long run. For example, Stiglitz, holder of the Nobel Prize, in economics wrote a book about how the euro is damaging to the EU economies. If Denmark stays out of the euro-zone it will have a much easier time if the euro-zone breaks down, than if it would have to pay all the transition costs to go back to DKK.
By staying out of the euro-zone, Denmark can have its cake and eat it too. On one hand, it gets the price stability thanks to the peg. On another, the peg could be suspended in the future. Denmark also avoids all the costs associated with the transition to using the euro notes, although this becomes less costly as the economy gets digital. The main downside is that this potentially opens DKK to speculative attacks.
The reason Denmark is not using the Euro is not because of economic reasons.
Denmark rejected membership of the eurozone at a referendum held on 28 September 2000. 87.6% of eligible voters turned out, with 46.8% voting yes and 53.2% voting no.
Have you read the Wikipedia article? I think it's probably better (more comprehensive) than any answer you will get here. It also lists some consequences (pros and cons) of the adoption of the Euro.
Theoretically it leaves room for independence of monetary policy. One may argue, the public wanted to maintain this flexibility, just in case it would ever be needed. On the other hand, making informed decisions on complex questions with only a binary choice are difficult to say the least.
So ultimately, the reason Denmark is not using the Euro is that enough voters were sceptical about the Euro (or whatever other reason they may have had to reject it).