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Well, I am personally biased toward Flying-types, since Flying = Birds, ya know.
But in battle, my favorite type has to be Steel since it has so many resistances – Normal, Ice, Grass, Flying, Psychic, Bug, Rock, Ghost, Dragon, Dark, Steel, plus Poison immunity. That's 12 all together. No other type even comes close.
However, Steel as an offensive move isn't so great, since it's only effective against Ice and Rock, and most Ice types are also Water so that cancels it out.
I guess Steel would be my favorite type defensively, and my favorite type offensively would have to be Fighting. Not only is it supereffective against everything Steel is, it's also effective against Dark, Steel, and the ever common Normal type. Plus if Focus Punch hits, it'll be sure to do a lot of damage to anything not resistant to it.
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