What does Boxing Day have to do with boxing?
c.1400, "harm, damage, danger," also "a harmful incident, misfortune, affliction," from Old French inconvenience "misfortune, calamity; impropriety" (Modern French inconvenance), from Late Latin inconvenientia "lack of consistency, incongruity," noun of quality from inconvenientem (see inconvenient). Later "impropriety, unfitness; an improper act or utterance" (early 15c.). Meaning "quality of being inconvenient" is from 1650s.
1650s, from inconvenience (n.). Related: Inconvenienced; inconveniencing.