This is a fun idea and I feel like there are a lot of cool ways to do it:
1. All for One’s quirk gives him taking urges so strong that he needs to hoard people. He’s not a very empathetic person and has no friends or family. So he picked a random guy who looks sorta like him to be the target. Easy enough to kidnap this family-less sickly guy and lock him up to make the voices stop. At some point All for One forgot that Yoichi wasn’t originally his brother.
2. All for One actually did lose a loved one, went nuts, and found a replacement in Yoichi. Except All for One was an only child. He lost his beloved white-haired pet dog.
3. Yoichi is actually All for One’s brother but he got amnesia and doesn’t remember. Bonus points if All for One accidentally gave him the amnesia.
4. Yoichi has a hidden quirk that makes strangers think that he’s related to them if he’s in danger. It’s a defensive ability so anyone who attacks him won’t kill him. (Like in my fic “A Murder of Brothers.”) Usually Yoichi’s ability only makes people think that he is their relative long enough for him to escape. But with All for One, he never stops being a danger to Yoichi so the quirk is always active. Yoichi can’t turn it off, and he’s TRIED.
5. All for One was separated at birth from his little brother, and went looking for him later. He found the wrong person due to a mistake in a DNA test. P.S. All for One's real brother is Hikage Shinomori who decided to become a hermit in the forest when he realized what he was in for if AFO ever figured it out.
6. Yoichi is All for One’s stepbrother but their parents only got married after they became adults so there’s no sibling bond between them. However All for One always wanted a little brother so he forced his way into Yoichi’s life. At first Yoichi tried to be nice about it until he realized that All for One was crazier than a dog in a cat factory.
7. All for One got seriously injured in a fight. While he was lying half-dead and with amnesia on the street, Yoichi rescued him and took him in. After All for One got his memories back he decided to treat Yoichi as family, and Yoichi had many chances to regret his kindness.
8. Yoichi is a deep cover government agent. His role was to pretend to be All for One’s long-lost brother in order to get close and spy on him. No one expected All for One to be so enthusiastic and clingy.
Yoichi: For the last time, I'm not your brother, I'm a spy!
All for One: For you, my dear little brother, I will forgive even your betrayal.
Yoichi: 😭
Government: You're doing great, you've been distracting All for One. Keep up the good work. No, we won't extract you.
Yoichi: I quit! I'm going to run off with a pair of vigilantes.