an idea perhaps supported by the German name

[kadioguy]

butterfly

[OE] A number of theories have been put forward as to how the butterfly got its name. Perhaps the most generally accepted is that it is a reflection of a once-held notion that butterflies land on and consume butter or milk left uncovered in kitchen or dairy (an idea perhaps supported by the German name for the ‘butterfly’, milchdieb, literally ‘milk-thief’). Other suggestions are that the word is a reference to the yellow wings of certain species of the insect, or to the colour of butterflies’ excrement.
https://goo.gl/5j5Eho
-----------
Why does it say 'an idea' instead of 'the idea'?
If I use 'the idea', is it acceptable?

 

[Matthew Wai]

It is an idea which was not previously mentioned, so 'an' is used.

 

[Tdol]

And it is one idea from a number of theories.

 

[Matthew Wai]

If I use 'the idea', is it acceptable?

'The' is acceptable in 'Perhaps the most generally accepted idea is that ...'.

 

[Raymott]

"... it is a reflection of a once-held notion (an idea ...)".

 

[GoesStation]

Perhaps the most generally accepted is that it is a reflection of a once-held notion that butterflies land on and consume butter or milk left uncovered in kitchen or dairy (an idea perhaps supported by the German name for the ‘butterfly’, milchdieb, literally ‘milk-thief’).
<SNIP>

If I use 'the idea', is it acceptable?

Only the indefinite article works there.