A torn rag fluttered on one's high horse (8)

I believe the answer is:

arrogant

I'm a little stuck... Click here to teach me more about this clue!

'one's high horse' is the definition.
I can't tell whether this defines the answer.

'a torn rag fluttered' is the wordplay.
'fluttered' indicates anagramming the letters (I've seen 'fluttering' mean this).
'torn'+'rag'='tornrag'
'tornrag' is an anagram of 'rrogant'.
'a'+'rrogant'='ARROGANT'

'on' acts as a link.

Can you help me to learn more?

(Other definitions for arrogant that I've seen before include "Haughty - imperious" , "Self-important and overbearing" , "Overweening" , "Overbearing; conceited" , "Over-cocky" .)

I've seen this clue in the Sydney Morning Herald.

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