Where does “other” come from?

Other comes from Middle English other, from Old English oþþe, from Old English ofþe, from Proto-Indo-European ánteros meaning the second of two.

other (English): See "other" below; Second; Alien

Definitions

other traces back through 3 separate lines of ancestry.

Step	Language	Word	Meaning
1	English	kin	Race; family; breed; kind; Persons of the same...
2	English	fictionkin	An individual whose personal identity is based in fiction of some kind: a fictional character, a fictional race or species, etc
3	English	fiction	Literary type using invented or imaginative...
4	Middle English	ficcioun	An invention or fabrication
5	Old French	ficcion	dissimulation, ruse, invention
6	Latin	fictio	fashioning, forming, formation; fiction
7	Latin	-tiō	tion, -ation, -ing
8	Latin	dissertātiō	(spoken) dissertation, discourse, disquisition
9	Latin	dissertus	arranged, disposed; explained
10	Latin	disserere	second-person singular future passive indicative...
11	Latin	dis-	asunder, apart, in two; reversal, removal;...
12	Latin	calceus	shoe
13	Latin	calx	limestone; chalk; the finish line
14	Ancient Greek	χάλιξ	small stone, pebble; gravel, rubble

Step	Language	Word	Meaning
1	French	autre	other; another
2	Middle French	aultre	other; another; someone else; another person
3	Old French	autre	Alternative form of altre; other
4	Old French	vie	life
5	Old French	viḍe	—
6	Latin	vitam	accusative singular of vīta
7	Latin	vīta	life
8	Latin	vīvō	to live
9	Proto-Italic	gʷīwō	live, be alive
10	Proto-Indo-European	gʷíh₃weti	to live, to be alive
11	Proto-Indo-European	gʷih₃wós	alive, living
12	Proto-Indo-European	gʷeih₃w-	to live

Step	Language	Word	Meaning
1	Middle English	oþer	other
2	Old English	ōþer	other, second
3	Proto-West Germanic	*anþar	second
4	Proto-Germanic	anþeraz	second; other
5	Proto-Indo-European	ánteros	other