The genetive case with negations implies absense or lack of something.
Жизни не хватит - here it implies that one life won't be enough for a particular purporse - lack
Also, знать means to have knowledge, have somehing stored in your mind etc, so it requires the genetive case after it if if you use it negatively.
Я не знаю слов - Look at that like this --- The words are absent from my mind or I don't have the words stored in my mind - absence
However, you still can say я не знаю слова, but this one would sound more general, like you don't know words at all
But, other verbs may not imply having something with their meanings. So they don't take the genetive case for their objects if you use the verb negatively.
For example:
Я люблю стол - Стол is in accusative
Я не люблю стол - Стол is still in accusative
That's because любить doesn't mean to have love but to be in love![]()