〜かねる
can't, be unable to (politely)
Verb ます-stem + かねる / かねます
Sign up free to review this point on a spaced schedule.
かねる is a polite, indirect way to say you can't do something, usually because it would be difficult, inappropriate or against the rules: その質問にはお答えしかねます, "I'm afraid I'm unable to answer that question".
It's a staple of customer service and business: ご要望には応じかねます, "we're unable to meet your request". It softens a refusal: the speaker could, in theory, but can't bring themselves to.
It also expresses hesitation about agreeing or understanding: その意見には賛成しかねます, "I can't quite agree with that".
The set phrase 見るに見かねて means "unable to stand by and watch". Don't confuse かねる with かねない, which means "could well happen".
Examples
その質問にはお答えしかねます。
I'm afraid I'm unable to answer that question.
申し訳ありませんが、ご要望には応じかねます。
I'm sorry, but we're unable to meet your request.
その意見には賛成しかねます。
I'm afraid I can't agree with that opinion.
見るに見かねて、手伝った。
I couldn't bear to just stand by and watch, so I helped.
彼の話は理解しかねる。
I find what he says hard to understand.