Alumnus is Latin that English never bothered to naturalise. It means "a pupil," but literally "foster son," from alere, "to suckle, to nourish" — the same root that gives alimony and, at a distance, adolescent. English took it in the 1640s and kept the whole Latin apparatus with it: the plural is alumni, the feminine is alumna, and its plural is alumnae. Most borrowings lose their native endings within a century or two; a word that keeps them is announcing that it was taken from the page by people who knew the grammar.
That is why the -us and -i endings are such a reliable cue. English is perfectly capable of saying alumnuses, and simply doesn't, in the same way it keeps datum and data, index and indices, criterion and criteria. The nourishing metaphor underneath is worth noticing too: a school's graduates are, in the word's own terms, the children it fed.
alumnus (n.) "pupil or graduate of a school," 1640s, from Latin alumnus "a pupil," literally "foster son," vestigial present passive participle of alere "to suckle, nourish" (from PIE root *al- (2) "to grow, nourish"). With ending akin to Greek -omenos . Plural is alumni . The fem. form is alumna (1882), plural alumnae . also from 1640s