As I understand it, the problem with nationalism is that it causes division and separation. Internationalism, on the other hand, recognises that we may speak different languages, have different customs, wear different clothes etc. but that we are fundementally the same. Nationalism can be used for political ends to stoke up suspicion and hatred.
In the First World War around Christmas 1914 the famous Christmas truce took place where French, German and British soldiers crossed trenches to exchange seasonal greetings and talk. They even sang carols together and played a football match. It must have been difficult for officers to persuade these soldiers to go back to killing each other after this type of contact had taken place.
You can read more about the Christmas Truce of 1914: