My best guess is that, they don't like being disturbed by humans.
you are the one who challenges them, If I was a mighty power legendary pokemon, who had found a nice place to rest I would be ticked.
I suppose being angry is supposed to make them appear very strong. I mean, wouldn't you think a wrestler gives the impression that he/she is strong by being belligerent and intimidating?
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If a bunch of no good lowly humans were always trying to either catch, abuse, or constantly misuse your power you'd be pretty ticked off as well. Examples of this are of coarse the Pokemon in the anime like Raikou & especially Mewtwo.
However, them displaying a constantly angry "look" is entirely subjective. I could say the exact same about several non legendary Pokemon like Salamence or Gyarados. My guess is that they look that way (legendary) because they were designed to be intimidating.
Rayquaza for example could be in a very good mood, but because it looks like an intimidating Dragon you could have trouble telling the difference.
N set by smalllady
If you mean Anime/Movies I say:
Mewtwo- Created by humans and constantly tested like a lab rat
Lugia- Was disturbed by that Bird collector guy and got all pissy (I can't remember the exact details, despite Pokemon 2000 being a favorite, the tape no longer working and my VCR just being ugh).
Deoxys- Someone else needs to fill that in, only saw the anime one, not the movie
Groudon and Kyogre- Getting awoken by Team Aqua and Magma then trapped inside their cages while their enemy is causing hell, they would be pretty angry.
Dialga and Palkia- Ah what was the deal with them again?
Darkrai- He has to be an angry Pokemon if he gives people nightmares
Giratina- His home was disturbed wasn't it? (It has been a while).
Arceus- Betrayed by a human so he's pretty peeved
Zekrom/Reshiram- Depending on what movie you watch, pretty much didn't know the world was going to end and acted on orders
Future movie- Haven't seen it but neither has the world yet has it:P
For the games.. Well they are always angry, some are the reasons above mostly getting disturbed in their homes. And like someone said, even Pokemon like Voltorb, Gyarados or Drapion always seems angry.
It's just like this, some were designed to look angry and intimidating and others, well, if you were forced to fight other creatures by lowly humans when all you want is to rest, you wouldn't be very happy either
I believe it was mostly a decision of the designers to make them look intimidating, since, well, they are supposed to be like game bosses and one of the game's biggest challenge. As for why Pokémon would behave that way it's probably due to the same reason - because they are powerful. I mean, most strong animals DO look intimidating. Sure, they may come across cute at times, but you don't just take a peek at, say, a shark and think "OMG KAWAII DESU". They scare you, and for a good reason. Keep the distance or they'll bite your head off!
Umm, would it have been a very good movie if Mewtwo had set Ash down for some snacks? No. They are made to look intimidating because the are powerful.
They're suppose to be intimidating as a sign of their true strength.
I always assume the reason why the majority of legendary Pokemon are angry is that they have become disconnected from the world they live in. They all are known to sleep for long periods of time, centuries or even millenniums in some cases. In that time the world around them would of changed immensely.
Imagine yourself as a kyogre, resting at the base of the sea. You would hear no noises of the world above you on land and no human could disturb you that deep down in the sea. After sleeping for hundred of years, a disturbance in your orb causes you to arise from your slumber. The world around you would be completely different. Whereas before humans were relying on Pokemon for transport, now they have metal machines to fly them in the sky, drive them around the land and dive to the depths of the sea. Can you imagine how confusing for them it must be to be forced into this new alien world?