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?
Related: Black Clover Teases A New Blade More Epic Than Asta's Four Swords
History inMy 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
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