But go against the Irish and get a bloody jaw
Preaching nonviolence but reminds of the scars

from Macklemore and Ryan Lewis – Irish Celebration Lyrics on Rap Genius

Meaning

They’re normally peaceful, but if you mess with them they will mess you up.

First line is a reminder of how troughout history the Irish people have always sought to fight back against their oppressors. The phrase ¨get a bloody jaw¨ accompanied by a punch gesture in the music video is without any doubt a reference to Ireland´s culture of boxing. As an example, more than half of Ireland´s Olympic medals are of boxing.

Katy Taylor winning the world´s first women´s boxing final at the 2012 London Olympics
The second line emphasizes the fact that the Irish manage to balance a very active remembrance of their bloody history (as illustrated below by one of the many poignant memorials that dot the country) not with grudge and the will for revenge but with the wisdom of non violence.

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