Warning! Spoilers ahead for My Hero Academia chapter 343!
All For One makes a startling comment during a rather longwinded monologue in My Hero Academia that could very well explain why Deku was born quirkless.
In the unofficial fan translation of chapter 343, All For One discusses a quirk that he stole from the ancestor of someone who's currently working alongside All Might against him. Of course, this could be anyone from a long list of heroes, but there's no one closer to All Might than Deku. But even if All For One did steal a quirk from one of Deku's ancestors, why would that make him quirkless?
History in My Hero Academia reveals that the vast majority of quirks are passed down genetically from parents to their children. Additionally, the reason why there are so many different types of quirks today is because of how much a quirk can change from generation to generation (which is also connected to the Quirk Singularity theory). Some popular examples are Shoto Todoroki's Half-Cold Half-Hot quirk that borrows an aspect of each of his parents' quirks. Then there are siblings who inherit the same quirk, but their powers manifest differently like Tenya who has engines in his legs as opposed to his older brother Tensei who has them in his arms. In other words, Deku's ancestor could have lost his quirk to All For One before he had the chance to procreate and pass on his powers to his children. He had nothing to give them. Although quirks are generally inherited, there are, of course, exceptions to the rule such as Eri's Rewind and Tomura's Decay. But this is rare.
Interestingly, this theory about Deku is an inversion of what Black Clover suggests happened to Asta. In a flashback from the devil Liebe, readers learn that Asta's mother was shunned by society since she possessed magic that automatically sucked the mana from anyone who came near her. So, it can be assumed that when she became pregnant with Asta, her power automatically removed all of his mana, resulting in him being born magicless. In the case of My Hero Academia, All For One may have indirectly made Deku quirkless if he did in fact steal the quirk from Deku's ancestor before his children could inherit his power. This would especially be the case if this unidentified ancestor married someone without any quirks. Although neither My Hero Academia nor Black Clover have justified these rumors, the latter is definitely more heartbreaking as it's easier to hate one's enemy for potentially ruining one's life rather than one's mother.
Regardless, in the case of My Hero Academia, All For One indirectly making Deku quirkless also means something else even more incredible. The fact that Deku was born quirkless allowed him to inherit the other quirks of his predecessors who once wielded One For All. Those who were born with a quirk and inherited One For All didn't have the ability to wield anything else, as it is akin to a cup that has ran over. Even though All Might didn't have his own quirk, he never received this ability since One For All hadn't evolved to a state where the current wielder could unlock the powers of their predecessors. Deku just came at the right time and can now wield far more than just two quirks. So, in essence, All For One not only stripped Deku of a quirk but made him into a more dangerous adversary. This is similar to how the villain accidentally made All Might immortal as revealed in an earlier chapter, taking the idiom "I am my own worst enemy" to a whole other level.