nonetiological

The story

1. Proto-Indo-European*né
2. Proto-Germanic*ne
3. Proto-Indo-European*ís?
4. Proto-Indo-European*h₁óynos
5. Proto-Germanic*ainaz
6. Proto-Germanic*nainaz
7. Proto-West Germanic*nain
8. Old Englishnān
9. Middle Englishnon
10. Old Englishnān
11. Old Englishnān-
12. Middle Englishnon-
13. Englishnon-
14. Proto-Indo-European*h₂ey-
15. Ancient Greekαἰτῐ́ᾱ (aitĭ́ā)
16. Proto-Indo-European*leǵ-
17. Proto-Indo-European*lóǵos
18. Proto-Hellenic*lógos
19. Ancient Greekλόγος (lógos)
20. Ancient Greekαἰτῐολογῐ́ᾱ (aitĭologĭ́ā)
21. Latinaetiologia
22. Englishetiology
23. Proto-Indo-European*h₂el-
24. Proto-Indo-European*h₂élisder.?
25. Englishetiological
26. English todaynonetiological

From non- + etiological.