Nationalism can absolutely be dangerous. In fact, there have been many instances just in the last century that show us how dangerous nationalism can be.
Nationalism inspires people to think that their country is superior to others. While this can simply lead to patriotism, it can also lead to aggression towards other countries and a lack of caring about other kinds of people. The worst example of this is, of course, the actions of Nazi Germany in World War II. In that instance, nationalism led Nazis to believe that they had the right to conquer other countries and to kill people that they saw as inferior.
Nationalism will not always be dangerous, but it certainly can be dangerous when taken to extremes.