It is directly addressed in DN 15 
https://suttacentral.net/dn15/en/sujato
‘Rebirth is a condition for old age and death’—that’s what I said. And this is a way to understand how this is so. Suppose there were totally and utterly no rebirth for anyone anywhere. That is, there were no rebirth of sentient beings into their various realms—of gods, fairies, spirits, creatures, humans, quadrupeds, birds, or reptiles, each into their own realm. When there’s no rebirth at all, with the cessation of rebirth, would old age and death still be found?”
“No, sir.”
“That’s why this is the cause, source, origin, and condition of old age and death, namely rebirth.
Extracting the abstract logic:
X is a cause of Y. What does this mean? Suppose there were no X, would there be Y?
“No, sir.”
That is why X is a cause of Y.
In modern parlance we would call X a necessary cause of Y. Necessary causation is about how the absence of something destroys an effect (but the presence of something does not guarantee the effect).
See also this very good essay by Ajahn Brahm:
Edit: In my own experience, the terminology necessary and sufficient is quite confusing, because the words necessary and sufficient don’t really explain what is meant very well. In my mind I think “necessary = effect destroyer” and “sufficient = effect creator”.
E.g. me writing this post is an ‘effect destroying’ cause for getting a like, because if I don’t write the post, there’s no way to get a like. The absence of post-writing destroys my ability to get a like.
But writing a post is not an ‘effect creating’ cause because it’s not guaranteed that writing a post will land me a like.
If I start smoking I gain an ‘effect creating’ cause of lung cancer. But if I don’t smoke, this isn’t an ‘effect destroying’ cause because I can still get lung cancer from asbestos or bad luck.