It's because Latin was the default language of scholarship and 'high' literature in 13th century Muggle England, and given the importance of (mangled) Latin for spells this would presumably hold true for wizards as well.
Also, if the piece is from Roger Bacon's diary, he definitely wrote in Latin.
If anyone can do non-wrong Latin, I could use a translation of the following for HPMOR. The original is supposed to be circa 1200.
No rescuer hath the rescuer.
No Lord hath the champion,
no mother and no father,
only nothingness above.