The phrase usually shows arrogance or a patronizing attitude rather than confidence. Don't be on your high horse just because you won the competition, humility is valued.
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Cultural Perception
Some cultures may view this phrase as highly offensive or disrespectful. In our office, being on your high horse can earn you a bad reputation.
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Informal Usage
This idiom is mostly used in informal situations and may not be appropriate in formal contexts. He's always on his high horse at parties, bragging about his new car.