きる and きれない: full completion and limits on what can be done
Distinguish completion with きる from the negative potential きれない. Compare not finishing with being unable to finish, and explore the difference in focus from 終わる.
Completing an action with nothing left
Adding きる to the masu-stem can emphasize completing an action or dealing with an entire amount. 長い小説を三日で読み切りました。 means that the speaker read the whole long novel in three days.
読み終わりました also describes completing the reading, while 読み切りました can highlight getting through the full length without leaving anything unread. Do not treat the two as opposite meanings that can never overlap.
Distinguishing きらない from きれない
食べ切れません。 means being unable to eat all of it. The potential form きれる is made negative, so 量が多くて、一人では食べ切れません。 describes an amount too large for one person to finish.
食べ切りません。 says that someone does not eat all of it. That form alone does not settle whether they are unable to finish or have chosen to leave some. 書き切れなかった describes a past inability to write something in full.
An extreme state or a firm assertion
疲れ切っています。 means being utterly exhausted. Rather than consuming a fixed quantity such as a serving of food, this use presents fatigue as reaching an extreme.
絶対に大丈夫だと言い切ることはできません。 means that the speaker cannot assert with certainty that everything is fine. 言い切る can mean making a firm assertion, so not every combination should be translated simply as finishing speaking.
Quick check: What was left incomplete in 時間が足りず、全部は説明し切れませんでした。?
Show the answer and why
There was not enough time to explain everything. し切れませんでした expresses an inability to complete the explanation; it does not also say that no explanation was started.