あながち〜ない
not necessarily, not entirely
あながち + negative (〜ない・〜とは言えない)
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あながち always comes with a negative and means "not necessarily, not entirely": 彼の話もあながち嘘ではない, "what he says isn't necessarily a lie".
It rescues an idea that people might dismiss too quickly. There's usually a hint that you thought it was wrong at first, but on reflection there's some truth to it.
Typical endings are 〜ではない, 〜とは言えない, 〜とは限らない and 無理はない ("it's not unreasonable").
It's close to 必ずしも〜ない, which is more neutral and logical. あながち has more of a "you can't just dismiss it" feeling. Don't use it with a positive verb: あながち正しい is wrong. And don't confuse it with まったく〜ない, "not at all", which is the opposite strength.
Examples
彼の話もあながち嘘ではない。
What he says isn't necessarily a lie.
その考えはあながち間違いとは言えない。
That idea can't necessarily be called wrong.
あの噂もあながち的外れではなかった。
That rumour wasn't entirely off the mark.
値段が高いものがあながち良いものとは限らない。
Expensive things aren't necessarily good things.
彼が怒るのもあながち無理はない。
It's not entirely unreasonable for him to be angry.