The insect, from Old English buttorfleoge, butter-fly, a compound so old that its motivation is genuinely lost, and so strange that every culture invented its own explanation.
Documented
The Old English record
Documented: buttorfleoge appears in Old English texts, with cognates across Germanic, Dutch botervlieg, German Butterfliege (alongside Schmetterling, from Schmetten, cream). The flutter-by reversal is first attested as a twentieth-century witticism, not an origin. The word is a butter compound. Why is unrecoverable.
Assessment: Documented: the OED and the Germanic cognates. The lost motivation is the documented fact.
Stories
The dairy thief
The leading folk explanations: butterflies were believed to steal butter and milk (the same accusation German Molkendieb and dialect names encode), or the common brimstone butterfly is butter-colored, or witches took butterfly shape to raid the churn. All are attested beliefs; none is provably the naming moment.
Assessment: Stories: the dairy-thief belief is documented folklore across northern Europe. Whether it named the insect or decorated the name is lost with the namer.
Interesting claims
The color of flight
The comparative note: languages that missed the butter connection named the insect from its motion or its soul, Greek psyche, both butterfly and soul, Latin papilio, Russian babochka, little grandmother. English's dairy insect is the odd one out, which may be exactly why it attracts rescue stories like flutterby.
Assessment: Interesting: psyche meaning both soul and butterfly is documented Greek. The archive files the flutterby myth as grief counseling for a weird word.
Sources and further reading
Oxford English Dictionary, butterfly: Old English buttorfleoge; Dutch botervlieg and German Butterfliege cognates
Bosworth-Toller Anglo-Saxon Dictionary, buttorfleoge (the Old English attestation)
Liddell-Scott-Jones Greek Lexicon, psyche: breath, soul, butterfly (the comparative note)
The flutter-by spoonerism, first attested as twentieth-century wordplay, not etymology (the myth's dating)
Worth asking
Why butter? The honest answer is that nobody knows, which is why the stories are so good.