かねる is a formal and somewhat literary way to say that you cannot do something or find it hard to do. It often implies that the speaker feels reluctant, hesitant, or finds it difficult to do due to circumstances. For instance, you might use it when you want to decline a request politely but firmly, or when you are unable to give a clear answer because you lack information or authority.

Unlike できない, which simply states inability, かねる carries a nuance of subjective difficulty or unwillingness. It is common in business settings and written communication, but it sounds stiff in casual conversation. For example, a store clerk might say 返品はできかねます (we cannot accept returns), which is more polite and formal than 返品はできません.

Note that かねる is not used with verbs that describe involuntary actions (like 見える or 分かる), because it implies a voluntary choice to refrain. Also, the negative form かねない means 'could easily happen' and is different in meaning.