It is not hair-splitting at all, it is what the Catholic Church teaches about the Mass.
Below is a link to the General Instructions of the Roman Missal (GIRM). In the Introduction the doctrine of the Sacrifice of The Mass is set forth and explained in much more detail than I can here with various references to Councils, Vatican II and Trent and the teaching of popes.

http://www.liturgyoffice.org.uk/Resources/GIRM/Documents/GIRM.pdf