Why did Celestia say someone needs to be optimistic to be a Princess?

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1,000 years is a damn long time if you're jaded and pessimistic. Optimism keeps your opinions of others high and keeps you working towards improvement while being willing to give the ideas of others a fair appraisal.

So I reckon it boils down to good health, for yourself and your nation.

Because optimism is arguably one of the most important traits anyone in a leadership role should have.

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Because people are stupid, even the well-meaning and good-natured ones. Being a (real) leader comes with having to deal with trying to get those people to understand you're doing something good for them, or that it might take longer than they demand and such. They're frustrating, patience-wrecking. That's just the people, there's situations involved in many cases you have no control over in trying to get what you need to help your people, which can totally fuck you over in your position and for your ability in doing what needs to get done.

If you're all depressed and short-tempered over years and years of this kind of crap, you can easily decide it's better to take shortcuts, to override the people who are trying to hold you back out of spite, and that way lies despotism. You don't even have to be an idiot to wind up on that path, or an intolerant jerkbag, you can be the kindest soul who's just had enough of having your hands tied by people who think they matter more than they do.

Personal mental/emotional health is also an issue here.

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What episode did she say that in?

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She said it in Magical Mystery Cure, near the end after Twilight became a princess.