Harry thinks he can't cast the Patronus. However, it turns out he can. He just needs to believe that death can be defeated, because Dementors are death in HPMOR.
"Holy shit Professor my Patronus is a man!"
"Yeah? Why is it naked, you little pervert?"
"It, uh, it's traditional in the natural sciences for humans to be naked! It means that I love science!"
He didn't say the 'Death will be defeated' part out loud because Dumbledore was there.
"Yeah, that's just what you'd say, you little shit,"
"Quirinus, is the verbal abuse necessary?" said Dumbledore.
"You're right, Albus, I'll tone it down," said Quirrell. "Well, Harry, why don't you tell us what it means that you love science?"
"It means, oh golly oh gee, that uh, one day science will discover space travel and cryogenics and then we'll all be, uh, immortal space gods with our own private stars, Professor!"
Harry hated how inarticulate he sometimes sounded outside of his own internal monologues, which were much more elaborate. One of these days he would have to sit down and write down his internal monologues in a coherent sequence.
"Yeah, and just who's going to do that? How are we going to get there, you egotistical little monster?"
"It'll be me, Professor, just because you think that I can't doesn't meant that I won't be the one to open up all of space for the betterment of humanity!"
"That's not fucking loving science, that's you wanting to fucking conquer the universe you little shit. Jesus Christ, Albus, you see why I shit all over this kid? He's a little monster. He thinks he deserves to conquer the universe and institute a galactic government because of how many times he's jerked himself off watching—burp—Carl Sagan's Cosmos."
"He believed these things before coming under your influence, Quirinus?"
"Jesus fuck of course he did. The universe is a dark and empty place, Albus. I believe that, you know that, blah blah blah the only meaning in life is what we make of it and also the eternal reward is what you'd say but fuck that. Who the fuck wants to become a space god? This kid was—burp—fucked long before he knew me."
Harry began to cry. He couldn't help it. His mentor was sneering at him.
"Are you sure you still wish to interact with him, Quirinus? It seems to exacerbate your drinking problems, and you are a good enough teacher that I would like to try and circumvent the curse on the position."
"Please don't take Professor Quirrell away from me, Headmaster."
"Sorry, Albus, we're—burp—codependent. Harry and Quirrell, Albus, that's us. Harry and Quirrell."
"You need help, Quirinus."
"Harry. Harry. We're breaking Bellatrix Black out of Azkaban! Bring your exhibitionism fetish Patronus!"
"W-why would we do that, Professor? Isn't she a murderer? Isn't she like You-Know-Who's right-hand woman?"
"Keep up, Harry, I'm telling you she was falsely accused by the establishment. Burp."
"Aw jeez Professor, b-but what if you're wrong? Won't this have like, I dunno, consequences?"
"Don't be stupid Harry, this is a plot tangent that won't go anywhere. We can do whatever we like."
Unfortunately, while this is a plot tangent, Quirrell tries to murder a prison guard. Harry stops him by throwing his naked man patronus into the way. Because of something something resonance in their magics, this knocks Quirrell out and gives Harry a headache
"Ugh, my head feels like a rat died in it," Quirrell said, holding his head as he stirred awake, "why the fuck did you do that, you idiot?"
"You were about to kill that man, Professor! I couldn't let you do that!"
"It's called a bluff, Harry, I shot a bolt of green light at him, that doesn't mean I was trying to fucking murder him. And he's a prison guard which means he's complicit in all—all this suffering, and he's basically a bureaucrat so he doesn't have a soul, and also probably an NPC. Now look what you've done! You've fucked up the whole plan and now we're stuck in fucking Azkaban with only half a plan to get out!"
"Do you—do you just not respect the sanctity of human life, Professor?"
"Gee Harry, what could—burp—possibly lead you to ask that question now. Not like I advocated for—burp—fascism in front of the whole school before Christmas or anything. Besides it's not like anyone who—burp—agrees to guard Azkaban has any respect for human dignity anyways so I'm doing the world a favor by getting rid of him. Now help me salvage this plan to break dear Bella out of prison, and also don't tell anyone that we did this."
Context: Hermione wants to be a hero, and so has decided to start an anti-bullying initiative, called SPHEW. Now, however, a bunch of bullies have ambushed the first-year girls with the intention of stopping them from stopping the bullying. Somehow.
"We don't need Harry Potter's help!" Hermione said. "Girls get it done!"
But then Harry appeared. "Bullies, prepare to be defeated!"
Harry did a thing. Most of the bullies were cowering at the sight of his high IQ. But one would not back down. His name was Lucian Bole, but he had the misfortune of crossing paths with Harry James Potter Evans Verres.
Harry bashed Bole's head into the floor over and over and over again. He didn't stop, even when Bole's face was disfigured. He only stepped away, breathing heavily, when Bole jerked for one last time and moved no more.
"Holy shit," Quirrell said. "Dude… did you just…"
"You did this to me, Professor!" Harry screeched. "I just wanted to go on adventures and do science! I didn't want anything to do with wizard fascism or Bellatrix Black or babby's first politicking! You did this to me!"
Hermione, SPHEW, and the faceless, nameless bully horde looked on in horror at Bole's unmoving body and the scene unfolding before them. Quirrell's eyes shifted between Harry and the audience to the spectacle of horror.
"Okay, calm down, Harry, don't say anything else you'll regret—"
"You knew I had a killer instinct the minute you saw me and you did nothing to stop me! Nothing! You said I should man up and solve things like a man instead of pretending to summon Azathoth! You said you wouldn't help me if I did things that way! Well guess what? I learned how to kill in ways that aren't useless! I hurt him and hurt him until he'd never hurt me again!"
For emphasis, he kicked Bole's corpse. "So who's laughing now, Professor? Huh? Huh?"
"Calm down, Harry. We can still fix this."
"Oh yeah, Professor? Huh? How are you going to do that? And why do you care? You don't give a shit about human life! These hands have killed, Professor! THESE HANDS HAVE KILLED!"
The next day:
"We are gathered here today," said Dumbledore, "to mourn the passing of Lucian Bole, at the hands of an angry centaur for disrespecting their sacred traditions. Students, I remind you once again to stay out of the Forbidden Forest, and also the Forbidden first and third floor corridors."
"Gee Professor," said Harry quietly to Quirrell, "is it really okay that we memory charmed everyone and also Professor Snape?"
"Harry. Harry. If you drop your omelet on the ground you—burp—you've already broken some eggs so you might as well break some new ones."
"I guess that makes sense."
This dramatic, wacky, and doubtless shocking turn of events was based off of Ender's Game, which is the inspiration for the wargames! But isn't this a romantic scene? Harry shows Hermione just what lengths he'll go for her!
Happy Valentine's Day!