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Izuku Midoriya's favorite thing is easily paradoxes and thought experiments.
For example, the Trolley Problem.
The Trolley Problem is a moral dilemma that presents the question of what you should do when a trolley is out of control, barreling down railway tracks.
Currently, the tracks are leading to five incapacitated people. You are standing by the switch that controls the way the track goes, much too far away to do much else, and you have to make a decision. Do you let the trolly kill five innocent people, or switch it?
Logically, you should.
However, if you switch the tracks, the trolley will go over the remaining person tied to the other tracks.
To Izuku, this problem is easy. He's too far away to save them (plus the original was made during the pre-quirk Era, so it didn't take that into consideration) so, it boiled down to one life verses five.
It's the same thing for the Hitler question.
Say, you could go back in time and you met a baby. This kids name?
Adolf Hitler.
Would you kill Hitler, who is now an innocent baby with no understanding of right or wrong?
It really just boils down to would you save millions of innocent lives for the price of one. Of course, there's the whole thing with time travel and the butterfly effect.
Would another kid turn out way worse? Would that kid go on and cause the end of the world?
His personal favorite though, is Schrodinger's Cat.
If you aren't familiar with it, it's a paradoxical thought experiment where a cat, a flask of poison, and a radioactive source are placed in a close box.
If the internal monitor detects the radioactive source being released, it breaks the flask, which releases the poison and kills the cat.
Or does it?
If they never open the box, the cat would be simultaneously dead and alive. Its dead, because it's been exposed to poison, but it's also alive, because there is no evidence of it being dead.
Theres also the grandfather paradox, where you can go back in time and kill your grandfather (for undetermined reasons) and your father/mother ceases to exist, therefore, so do you.
So you can't go back in time to kill your grandfather, who is now alive, and has given birth to your father/mother who created you, giving you the ability to kill him, and you do.
To Izuku, it's thrilling.
Izuku loves to rip people apart, piece by piece. He loves watching them squirm as he not so subtly points out their flaws, watching their body language show just how uncomfortable they are.
As a kid, he hated when people lied to him, so he learned how to get the truth out of them.
He's amazing at analyzing, so why?
Why can't he tell what Nezu is thinking?
They were dismissed for lunch a few moments ago, and thank fuck, because Izuku was starving.
"And Midoriya? Come with me." Aizawa says randomly and everyone in the room shares a confused glance.
"Um, okay?" He agrees hesitantly, slinging his bag over his shoulder.
Aizawa proceeds to lead them up a couple stories and down several halls and Izuku is yet to figure out why.
He hasn't asked, of course not, but Aizawa is also yet to say anything.
A few more minutes pass and they're at a door.
Aizawa goes to knock but the door swings open, much to Aizawa's dislike, to reveal the principle.
It's now that Izuku realizes he's never seen the principal before.
He never attended the assembly (thanks Eraserhead) and since Nezu doesn't deal with defeating villains, he never had an urge to look him up.
So excuse him for not expecting… this.
The principle is not human, that much is obvious.
He has white, clean fur (does he groom himself?) and a long scar across his right eye. His head and tail are reminiscent of a mouse, but he looks more like a tiny bear.
"Good afternoon, Aizawa!"
His teacher huffs before walking in. Izuku follows suit.
"Take a seat," the bear(?) invites, so Izuku tries.
He tries , but he ends up locking eyes with him.
Nezu's tail swishes painterly, thumping against the seat and they're both suddenly trying to rip the other apart.
Nezu's beady eyes bore into his, cold and calculating. Izuku's stared back.
"Oh how astounding!" The principal cheers, the first to break eye contact and his smile growing.
Aizawa shudders and Izuku blinks.
"Would you like tea?"
What a blatant change of topic.
"Um, yes please."
"Wonderful! How about you, Aizawa?"
"No thanks."
Nezu hums, pouring himself and the student a cup.
"Um, please sir, why am I here?"
"Because I think you're rather intriguing, Midoriya." He says vaguely. "Tell me, what creature am I?"
Izuku thinks for a moment. "I don't think your breed has a specific name, seeing as you were experimented on." He says, deciding on his answer. "But from what I can tell, you're a cross between a bear and a mouse. There's no way you're just one or the other, seeing as your face structure and tail indicate mouse but almost every other part about you screams bear."
Nezu's grin somehow increases even more.
"So I'm a hybrid species then?"
"Well, yeah. Probably."
Nezu takes a sip of tea and Izuku does the same. "But what about my human aspects?" The former presses, and Izuku's brain immediately understands.
"What's human about you, though?"
Nezu's excited, the greenette notices as his grin borders feral.
"Oh how magnificent! It seems this was worth my time! Would you mind meeting me here tomorrow during lunch?"
Izuku stares at the hybrid for a long moment.
"Okay," he says, unsure of what he's actually agreeing too, "okay."