〜とは裏腹に
contrary to, at odds with
Noun + とは裏腹に / と裏腹に
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とは裏腹に means the reality is the opposite of what was expected, said or shown: 期待とは裏腹に、結果は散々だった, "contrary to our hopes, the results were dismal".
The noun is an expectation, a statement or an appearance: 期待, 予想, 言葉, 表情, 発表, or 明るい性格. The second half reveals the contrasting reality.
It's close to に反して (N2), "contrary to". 裏腹 literally means "back and belly", two opposite sides of the same body. It's especially good for a gap between words and feelings: 言葉とは裏腹に、彼女の顔は悲しそうだった, "her face looked sad, despite her words".
Compare に沿って (N2), "in line with", which is the opposite relationship.
Examples
期待とは裏腹に、結果は散々だった。
Contrary to our hopes, the results were dismal.
言葉とは裏腹に、彼女の顔は悲しそうだった。
Despite her words, her face looked sad.
予想とは裏腹に、試合は一方的な展開になった。
Contrary to predictions, the match turned out one-sided.
明るい性格とは裏腹に、彼は繊細な一面を持っている。
Behind his cheerful personality, he has a sensitive side.
政府の発表とは裏腹に、生活は苦しくなる一方だ。
Contrary to what the government says, life just keeps getting harder.