So I revised it. Here's the revised story.

Karkat leaned back on the couch in one John Egbert's house. They were watching a horror-slasher film of some kind or another and Karkat really didn't see the point in such idiocy. But he shuddered at the equivalency the slashers had with sobered up Gamzee Makara.
"WHY DO YOU HUMANS LIKE SUCH PITIFUL ENTERTAINMENT SUCH AS THIS 'TEXAS CHAINSAW MASSACRE' MOVIE YOU HAVE BEEN RAVING ABOOUT, EGBERT?" Karkat looked over at John but realized his words were lost on the boy; he was transfixed on the movie. The Troll scoffed and looked away. He could be needy for affection and attention without ever revealing that he was; and currently he was needy. He'd never say it aloud but he did enjoy the human's company.
Karkat dozed off and was nudged awake at the end of the movie.
"Karkat, did you really fall asleep?" John looked disappointed.
"YES. IT WAS A STUPID REPRESENTATION OF A SERIAL KILLER AND HAD NO PLOT OTHER THAN TO KILL YOUR LOT OF PEOPLE."
"He was human, too, Karkat," John made a face.
"AH WELL. THAT MAKES HUMANS EVEN MORE STUPID. WHY CREATE A MOVIE BASED ON THE SLAUGHTER OF YOUR OWN PEOPLE BY ONE OF YOUR PEOPLE?"
"It's called horror for a reason, Karkat." John sighed and stood up, stretching as did so. "You probably just didn't like it because it reminded you of Gamzee."
Karkat looked taken aback. "WHAT DID YOU SAY?"
John looked at Karkat. He knew that Karkat heard him. "I said you didn't like it because it reminded you of when Gamzee went bat-shit crazy because he wasn't stoned."
Karkat picked up the Heir of Breath and slammed him against the wall. "SHUT UP EGBERT!"
John was 17, and he had grown tired of Karkat's horrible behavior. "Dude. You are 17 Earth years old. You need to grow up. You and Gamzee don't have a moirallegiance anymore, or whatever you call it. You severed that when Gamzee sobered up. Wasn't it you who told me when a bond is severed to let it go?"
It was then that John saw a softer, more desperate side to Karkat. The red fluid pooled up around his eyes and leaked out as he looked totally lost. John and his friends had a major influence on the trolls; who now shared their range of emotions.
Karkat slowly set John on the ground before punching the wall nearby. "DAMMIT. THIS ISN'T FAIR. WE'RE SUPPOSED TO BE KISMESIS. EQUAL HATE TOWARD EACHOTHER! BUT IT'S NOT EQUAL AT ALL."
John remembered that Kismesis was a sort of arch-rivalry. "Why isn't it equal hate?"
Karkat looked down and gritted his teeth. "BECAUSE I SEEM TO HATE YOU LESS THAN I WOULD LIKE, EGBERT!"
"Then... ah... maybe we should move into a moirallegiance...?"
Karkat scoffed. "IT'D BE DIFFICULT WITHOUT AN AUSPISTICE, YOU SPECKLE-FACED GARDENTRUMPER."
John sweatdropped. "Then maybe we can sort this out by having Rose be the auspistice...?
Karkat looked down. "POSSIBLY, IF SHE ISN'T TOO CAUGHT UP IN KANAYA."
"So what... wait until she's available just to inevitably doom ourselves into a forever caliginous relationship?" John pouted.
"THAT'S HOW IT WORKS, EGBERT," Karkat brushed him off.
John sighed out. "Not for us humans! We don't follow your 'Quadrants' of romance. We don't follow: kismesis, matesprit, or whatever! We follow what our hearts tell us, not our rules and standards!"
"BUT I'M A TROLL-"
"I don't care! You're mixed with us 'pathetic humans' now, so there's gonna be give in take. What you see as 'kismesis', I see as friendship. What another troll sees as 'matesprit', I see as 'love'. And there's nothing wrong with that in our language!" John frowned.
"WOW EGBERT. DON'T GET TOO EMOTIONAL ON ME NOW," Karkat smirked.
John made a frustrated noise. "You know what? I give up. I don't want any part of your 'Quadrants' or whatever. I don't wanna be your kismesis, I don't wanna be your moirail, I don't wanna be your anything!" He activated his power over wind and floated away, angry.
Karkat stopped and stared at John, wide-eyed. John had more hate for him than he had for John. There was no kismesis; John severed it. Trolls hate losing their Quadrants, no matter the relationship. Karkat especially hated losing a caliginous crush that had the potential to become a flushed crush with proper auspisticism.
"EGBERT...?" John was long gone.

A couple days later Karkat sat on the edge of building, legs pulled to his chest. He hadn't seen John since he severed their kismesissitude. Karkat noticed a shadow and stood immediately, getting his strife specibus ready. He relaxed when he saw it was Rose.
"YES?"
"John told me you guys had a fight, so I came to analyze the situation in order to repair it."
"I'M SURPRISED YOUR NOT SNOGGING WITH KANAYA."
Rose gave a soft chuckle. "I would, but John's my friend... or as you Trolls would call it, my moirail."
Karkat looked away. "I SEE."
"So... John's harboring black feelings and you're harboring red feelings. It would have been fine had you not started feeling those red feelings. Am I right?"
Karkat gave a slight nod. "ARE YOU JUST GONNA ANALYZE?"
"No... I was encouraged to partake in your culture's auspisticism."
"BY KANAYA?"
"Who else?"
Karkat sighed. "SO WHY ALL THE QUESTIONS?"
"If I'm gonna do this auspisticism right, I need all the info from both sides. So lay your feelings on me: human and Troll."
Karkat gritted his teeth. The need to have his Quadrant fixed with John was dire so he laid it on Rose. "YOU'RE RIGHT. I HAD BLACK FEELINGS FOR JOHN, BUT IT DIDN'T FEEL RIGHT. I KNEW HE HAD RED FEELINGS FOR ME. THEN I DEVELOPED RED FEELINGS FOR HIM AND THEN... HE DEVELOPED BLACK FEELINGS FOR ME... AND I JUST CAN'T ADJUST MINE TO BE BLACK AGAIN."
"I see... maybe his aren't truly black feelings. Would you guys like to have a Red Romance or a Black Romance...?"
Karkat looked up. "I THOUGHT I WANTED US TO BE CALIGINOUS. BUT... I WANT US..." He trembled. "SCREW THIS, I DON'T NEED HIM!" He walked away. He wanted him and John to be flushed, now.
"Interesting, I see..." Rose smirked.

In another area, John was pouting in what he thought was a tree. He looked up at the sky before readjusting his glasses. He looked over when he heard his name. He floated to the ground.
"Hey Rose, sup?"
"I'm playing auspistice."
"Oh... for who?"
"You and Karkat."
John made a face. "Why. I ended any Quadrant we would have had."
Rose smirked. "But you have red feelings for him don't you?"
"Red feelings..? Screw Troll talk!" John grabbed out his Zillyhoo and smashed the tree-looking thing, earning him lots of Grist and a couple Boondollars.
"Calm down. I'm saying you like him!" Rose snickered as the Grist was collected.
"Of course I do, I'd like to consider him my friend!"
"John, you know what I mean. You like him like I like Kanaya," Rose pointed out.
John's face heated up and looked down. "Well... yeah, but... he wants to push us into being enemies so bad it kinda just... hurts... and then when I open myself up, he laughs at me... Dammit. Why couldn't trolls have more human emotions." He teared up with clear fluid that humans possessed.
Nearby, a once-angry Karkat listened, hidden from view. Like? He understood it, but... Rose and Kanaya were matesprits. Did that mean John wanted to enter a matespritship with him?
"It's just... so confusing..." John sighed and slumped near a tree.
"Well I'm gonna find Karkat, you guys should talk this out with me here to mediate," Rose nodded.
"Ah... right... you're the auspistice or something like that..."
Karkat made himself scarce before Rose could find out that he had been spying on them.
Moments later he reappeared with Rose.
"Alright. I'm not too sure on this auspistice thing or if vacillation is possible with only two partners and one of them being a human, but we're gonna try to vacillate this... awkward quadrant into a happy moirail or matesprit, whatever you two decide," Rose stated as she looked at Karkat. "Karkat here wants to enter a matespritship with you, John, and from what I here, you wish the same. Is all this correct?"
Both parties nodded with blushes on their faces.
"Good. But there's some unsaid feelings from John that needs to be said. I don't think you'll say them until he does, Karkat," Rose stated.
"Karkat... look... in human terms, I really like you... but you don't try to understand my view of how I view our relationship. And it's frustrating," John began.
"BECAUSE IT'S STUPID."
"There you go again!" John angrily grabbed at Karkat's horns and tugged.
"OW! EGBERT, WHAT THE FUCK!?"
"Geez... and you never call me by my first name..." John let go and looked to the side.
Rose sighed. "John, be nice. Karkat, call him by his first name if you want a matespritship."
Karkat looked down before scoffing. "JOHN..."
The Heir of Breath's heart beat at that, but he wouldn't say a word, just blush.
"JOHN. YOU SHOULD LET ME FUCKING FINISH MY WORDS BEFORE PULLING ON MY GODDAMN HORNS. THAT SHIT HURTS."
John nodded. "Fine then, enlighten me why my views are so stupid."
"I WILL. IT'S STUPID BECAUSE YOU PRATTLE ON ABOUT LOVE AND TRUE LOVE. BUT WHAT IS LOVE? I LOOKED IN YOUR STUPID HUMAN DICTIONARY AND YOU KNOW WHAT I FOUND AS THE DEFINITION?"
"Do tell me, Karkat," John stated, not happy.
"LOVE IS 'AN INTENSE FEELING OF DEEP AFFECTION'. THAT'S SO IDIOTIC!" Karkat.
"What's wrong with deep affection?"
"IT'S NOT PERMANENT. YOU KNOW WHAT MATESPRITSHIP IS?"
"Well, no... you never told me what it was, how was I supposed to know?" John frowned.
Karkat sighed and facepalmed before blushing, "MATESPRIT IS EQUIVALENT TO WHAT YOU HUMANS REFER TO AS SOULMATES!"
John blushed immensely. "Ah... oh..." He looked up, glasses fogging up. "I... didn't know..." He laughed a little before looking to the side. "Now that you put it that way... love... seems almost pathetic compared to matespritship, but you know... I'll still believe in what I believe in because my view of love IS permanent."
"HOW?!" Karkat was getting frustrated.
"There's a technical definition for love, yes. But how I define love is different," John stated.
"THEN TELL ME HOW YOU DEFINE LOVE," Karkat demanded impatiently.
"Love is an intense feeling of a deep affection that lasts a lifetime," John smiled at Karkat.
Rose had already left, her job as auspistice was done. They were on their merry way to vacillating into a matespritship.
Karkat blushed and looked away. "SOUNDS LIKE A HUMAN WAY OF SAYING MATESPRITSHIP."
John giggled and leaned forward, closely to Karkat. Karkat's eyes widened as he blushed more intensely. "CAN I HELP YOU, EGB- ER... JOHN?"
John's heart beat again. "So does this mean we've mutually agreed to enter a matespritship?"
Karkat scoffed. "YEAH, SURE."
John smiled and kissed Karkat's lips. Karkat was surprised, but kissed back, holding his matesprit close to him.
If something happened to John, he knew that he wouldn't make it alive. He'd most likely go Gamzee on whoever killed his matesprit before claiming his own life in despair. It's how he was. He cared deeply for this human and this human was his, no one else's.
Karkat pulled back and gave a smile for once. "THANK YOU... FOR BEING MY MATESPRIT."
"I've wanted to for a while now... but you had those black feelings for me..." John blushed.
Karkat kissed the top of his head. "I HAVE RED FEELINGS NOW."
"I see."
They kissed once more. Karkat couldn't have been a happier troll and John couldn't have been a happier human.

I mean it's not completely revised.
Just some of the errors were fixed.
Like when Karkat was speaking towards the end, I forgot to capitalize every word.
Or a few letters were lopped off.
It's fixed now.
I hope you enjoyed my first Homestuck Fanfiction! :D

Your author,
Nova