Question

Why is Outrage a Dragon-type move?

Comments

Honestly I'd say this is a result of information being lost in translation.  Similar to how we, in English, refer to it as Steel Type, but in reality it should have been Metal Type.  Also Dark Type is, in Japan, Evil Type, referring to the cultural folklore about dark spirits.

Answer 1

Dragon types are usually regarded as very destructive, arcane creatures and Pokémon. Think about typical dragon myths; a dragon goes on a rampage until someone can stop it. Outrage is likely a Dragon type move because of dragon's violence and power. The move description from SwSh is:

The user rampages and attacks for two to three turns. The user then becomes confused.

Sounds a lot like common depictions of dragons.

A Pokédex entry from the original Dragon type (Dragonite) states:

Moon: Incur the wrath of this normally calm Pokémon at your peril, because it will smash everything to smithereens before it is satisfied.

Oodles of Dragon type Pokédex entries mention this disastrous trait.

Haxorus

Shield: While usually kindhearted, it can be terrifying if angered. Tusks that can slice through steel beams are how Haxorus deals with its adversaries.

Salamence

Sun: When angered, it loses all sense of itself and destroys everything around it. The destruction will continue until Salamence has tired itself out.

Hydreigon

White: The heads on their arms do not have brains. They use all three heads to consume and destroy everything.

The list goes on. The terrifying qualities of Dragons and their angry reactions are probably why Outrage is a dragon type move in Pokémon.

Answer 2

The Japanese name げきりん (逆鱗) gekirin ("wrath of one's superior", literally "reversed scale") may refer to the idiom 逆鱗に触れる gekirin ni fureru ("to infuriate one's superior", literally "to touch the reversed scale"). In East Asian mythology, dragons are benevolent and tameable creatures, but possess a scale growing in reverse (some sources say, on their chins) which, if touched, will incite the dragon's fury.

source
Also it's because of Game Freak logic.