Dragonflies should obviously be bug/dragon, but the two that exist are Dragon/Ground and Bug/Flying :/
Actually, the only dragonflies in Pokemon are Yanma and Yanmega. Trapinch, Vibrava, and Flygon are based on the antlion (also known as the doodlebug).
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Trapinch is based on the larval form of the antlion. It's a bug that digs a pit in the sand and waits at the bottom of it underneath the sand, with only its jaws exposed. When an insect falls in, it flicks sand at it to knock it down, then drags it underground and eats it.
Once it's eaten enough, it turns into a pupa for a time, then emerges as an insect that looks a lot like a dragonfly, but with a flexible tail. It uses that tail to mate...OK, let's just leave it at that. Point is, they look similar to dragonflies, but they're completely unrelated. Also, they don't eat as adults, so they usually die after a few weeks...poor Flygon!
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Sorry if I seem like I'm being a know-it-all. Antlions are just some of my favorite animals. Personally, if we get another bug type, I'd like it to be a dragonfly line that actually makes sense. GameFreak doesn't seem to know it, but dragonflies actually start out life living in the water, where they hunt fish and tadpoles. A Yanma prevo with a branching evolution, perhaps?
See those mouthparts on the front of his head? Yeah, those actually extend and pierce things like harpoons. Think about that and tell me that wouldn't make an awesome Pokemon.
Bug in general is just a seriously underdone type. I don't get why GameFreak appears to have run out of ideas for new arthropod-based Pokemon. They've made like three moths, and I'm still waiting for cockroaches, sowbugs, ants, and most of all, centipedes. Oh, and a spider line that isn't an embarrassment to its own species.