Ok so this is the backstory of the Hero's and Villains childhood together.

DabiHawks

Dabi and Hawks were best friends in grade school and would always hang out.

Then they would hang out a little bit because Dabi was busy training with Endeavor (Dabi is Touya Todoroki) and when Hawks would ask he said that he was babysitting his siblings and Hawks believed him.

It was until a few weeks when Hawks saw the burnt marks on Touya 's arm.

Hawks would as everyday what was going on at home and Touya would say nothing.

Eventually Touya and Hawks had a big fight on how Touya would hide stuff from Hawks.

The decided to not be friends anymore.

A few days later Hawks have learned that Touya have ran away and he felt like it was his fault.

Togaraka

Toga and Ochako friend thing started on the playground.

People wouldn't play with Toga because of her quirk and people wouldn't and play with Ochako because they were scared that she would float them to the moon.

One day Ochako saw Toga crying on the swings and she went up to her.

Toga to her about Ochako about her quirk and Ochako to Toga about her quirk.

They started to play with each other on the playground.

They would play with each other every other day.

Togas parents disowned her because of her quirk except her brother (monoma) so they would sometimes sneak out of the house and go to Ochako's house.

Toga and Ochako were best friends up until middle school. 

One day Monoma asked Ochako if she'd seen Toga because she was missing.

They spent weeks trying to find Toga.

One day when Ochako was walking through a valley she saw that Toga killed someone.

She confronted her and nevered talked to her again but never told the police because she loved Toga.

Now last but certainly not least

Dekubaku

When Izuku and Bakugou were young Izuku didn't have a quirk so Bakugou made fun of himself when they were young and when they were in middle school.

Bakugou and his friends would bully Izuku.

It was wasn't until the middle of the school year, Izuku quirk came in.

Now that's a little weird but that's when he discovered Villain Deku so now he have a quirk.

One day Bakugou was out because he was sick so Izuku thought that is was time he would show is new quirk to Bakugou's friends.

When Bakugou came back to school he saw that his friends we're having out with Izuku.

He was jealous so he want up to Izuku to blast his quirk at him but Izuku used his new quirk to stop him.

Ever since that day Bakugou was named as weak and Izuku was stronger than him but he didn't let that get to his head.

It wasn't until Izuku and his new friends (Bakugou's friends) started bullying Bakugou.

Then one day Bakugou learned that Izuku was go to sign up for UA and that made Bakugou mad because he knew with Izuku's new quirk that he was going to be accepted.

So one day Bakugou asked for Izuku to come to the roof along.

Izuku did but he didn't see Bakugou then he felt someone pushed him off the roof.

Bakugou did and he left the scene.

But lucky for Izuku Kurogiri was there to save him.

Ever since that day Izuku wanted revenge but didn't want to kill him like Bakugou attempted to do.

He wanted to make Bakugou his PET