The Pervy Ninja hero "Pussy Smasher"

The pervert is lucky?

All Might, you are committing a great mistake I am not what you-"

"YOUNG MIDORIYA! YOU HAVE PROVEN YOURS-BLHEEERGH!" Before All Might could finish speaking, he vomited blood.

"W-Whoa you alright pal? You might have vomited an entire lifetime over there!"

"Y-Yes I'm fine, for you see, this is in fact my true form." All Might, who was now a skinny skeleton told Midoriya.

"What are you, Freeza?"

"No! Not like that, I mean, this is my real form, I can't afford to use my quirk for more than 3 hours, all due to this injury:" All Might, a now skinny old man, lifted his shirt to show a terrifying scar in his abdomen.

"O-Ouch."

"Because of this, I grow weaker every day, and soon, I won't be able to be this world's symbol of peace anymore, but luckily, my quirk can be passed on!"

"Ok, I think you finally starting to answer my questions..."

"My Quirk's name is One-For-All, a power passed through generations that I inherit to become a hero, and you, Midoriya Izuku, is the one who I want to pass it to!"

"Wait hold up man, you just met me."

"Precisely, and the action you've done earlier proved everything that the media and my fellow pro-heroes said otherwise. You, my young man, is called "The Quirkless Human Cockroach of Mustafu". But you are no cockroach, you were the true hero there. That young man you've saved, Bakugou Katsuki isn't it?

"Y-You know about him?"

"He has a feed insulting you on Twitter."

"Ah that... wait you have a Twitter account?"

"Don't tell anyone about it."

"Sure thing, All Might."

"Well, getting back to the point, he despised you and yet you've saved him, the world hated you but still put your life on the line for it, you, my young man, is worthy of becoming this world's next Symbol-of-Peace!"

"Sike. Impossible. Me? Midoriya Izuku? Look, you are wrong pal. I'm not worthy! I'm a god damned pervert!"

"And yet, you still saved the day and worried about others' well being."

"No, no no no no no. All Might, I am THE pervert. I am human garbage I can't-"

"Don't you ever call yourself that. If you really were garbage, Young Bakugou would've been possibly hurt, but you've saved him. Without the need of a quirk, nonetheless."

"Sure, sure, I still have a positive humanity on me left, but that doesn't translate to: I am this world's purest person and can become its top savior. I am the least man likely to be a hero! People would hate me!"

"You have proven to me you don't care what people think of you."

"You are not gonna give up are you?"

"Nope."

XXXxxxXXX

And then, Midoriya was forced to be trained by All Might, sure, he may be superhumanly resistant, but his physical strength is still low! He lost one entire week of girl hunting for this hell!