Well without getting into it too deeply so as to go way off topic. But the term 'paddy', like 'mick' and 'taig', is a term used -- usually derogatorily -- in regards to Irishmen. When put in the context of 'threw a paddy', which is meant to describe irrational, violent, fighting, fit-throwing behavior, it is an ethnic slur, i.e., you are describing 'typical' (re stereotypical) Irish behavior, for the stereotype of the Irish or 'paddys' is to be fighting, violent, ill-tempered etc. Terms like 'paddywagon' also stem from the stereotype of the drunken Irish and that the drunk wagon would be filled with 'paddys' or Irishmen, or that the cops would have to go round up the drunken Irish at the end of the night. 'Acting the mick' is another common ethnic slur based on the Irish stereotype. Words like Mick, Paddy, Tim and Taig are used to refer to Irish people (like Jose or Juan for Mexicans) because the names were at one point very common for Irish men, especially at a time when they were a large part of the immigrant make-up either in the UK or in America. Taig stems from Tadgh which is the Irish name for Timothy and it is a very offensive term.
Anyway, I was just surprised to see 'threw a paddy'. Without wanting to get too PC, describing behavior in racial/ethnic terms is awkward to say the least, and on a UK based forum where a number of people are Irish or married to Irish or in Ireland and aware of the history of British stereotypes of Irish people and its legacy...well, I suppose that is me getting too PC but I just thought it was worth questioning the use of.
