Irish and German Americans were vocal in their opposition to America joining the Allies. Germans for the sake of their old country and the Irish because of England's role in Ireland. TR saw this as a danger to what he believed was a necessary American involvement in the Great War. So he attacked the concept of hyphenated Americans as those who felt America should make policy decisions based on how they would help or hurt their homeland.
Now we think of the idea of hyphenated Americans in terms of people demanding separation and special treatment for their culture. That was not the meaning 90 years ago.
"He spoke these words to a meeting of the Knights of Columbus, the well known Catholic men's group. At the time this group was mostly made up of Irish and German American Catholics, as Italian and Polish Catholics were still in their first generation."
That makes this even gutsier! He said it to the faces of the people he was talking about. What balls!
My own german ancestors had lived in german speaking communities in Pennsylvania. About the time of TR's presidency, they quit speaking German in the home, and switched to English.