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Because they look cool.
I'm more of a dinosaur guy but dragons are alright. From a "dragons are cool" standpoint I like that Tyrantrum, the T.Rex Pokemon is a Dragon but it gives him a bunch of weaknesses I would've preferred he not have in addition to the already bad Rock typing. Lots of people also really liked Dragalge after it got its Dragon typing, it just adds "cool" points in general. I personally got a little annoyed that Scrafty and Scraggy are in the Dragon egg family since I think they're ugly fucks who besmirch dragons but that's just me.