It’s hard to imagine now, but All Might originally rejects Deku and does not offer him any hero-advice. Why did All Might reject Deku?
All Might chooses to reject Deku because he didn’t have a quirk. At the time, All Might was doubtful that someone without a quirk could be a hero.
He suggests that Deku could become a police officer if he still has the itch to help people.
All Might chooses to reject Deku
In chapter #1, Deku meets All Might for the first time. The #1 hero saves Deku from a slug-type monster and does not stay for conversation afterwards.
Hoping to speak to All Might and ask a few questions, Deku latches on to All Might’s leg as he flies away. Not wanting Deku to fall, All Might lands on a local building’s rooftop.
All Might is in a rush to leave as his quirk is acting up. Since he suffers a grave injury against a foe in the past, All Might is getting weaker. He can only do a few hours of hero work a day.
Before All Might blasts off, Deku asks if it’s possible to be a hero without a quirk. As Deku continues to explain that he wants to become a hero since he thinks it’s the coolest thing someone can do, All Might reverts back to his skinny form.
All Might says that a pro should always be ready to risk their life. Without power, All Might explains, it’s doubtful someone can be a hero.
“If you desire to help people, becoming a police officer is always an option,” All Might says. “Those Villain Custody Officers are often mocked, but that too is admirable work.”
The pro hero says it’s not wrong to dream as he enters the building staircase. He says that Deku needs to be realistic in spite of dreaming.
So that’s the answer. All Might initially decides to reject Deku because he’s doubtful someone without a quirk can be a hero. He is not planning at the time to make Deku his successor and just sees him as a random kid.