The phrase "comes down from a high horse" refers to someone who has been arrogant or haughty and has finally humbled themselves. The antonyms for this phrase would be "stays on their high horse," meaning they continue to act superior, or "remains arrogant," meaning they refuse to change their behavior. Alternatively, "humbles themselves" or "shows humility" would be antonyms for the original phrase, indicating that someone is willing to acknowledge their mistakes and learn from them. It is important to remember that being humble and kind is always better than acting superior, and we should all strive to treat others with respect and compassion, regardless of their status or situation.