Why do some Hermione and Harry shippers say that when they go to the graveyard, it was romantic?
Because it is.
You can interpret it however you like, but it doesn’t change the fact that It’s a lovely piece of Gothic romance.
The kind of emotional support that Hermione provided for Harry was more than mere friendship, and more than what a sibling might provide (and, in a sense, he was taking her to meet his parents—a time honoured romantic tradition).
DH ch 16: Hermione's voice came out of the blackness for the third time, sharp and clear from a few yards away. "Harry, they're here... right here." And he knew by her tone that it was his mother and father this time: He moved toward her, feeling as if something heavy were pressing on his chest, the same sensation he had had right after Dumbledore had died, a grief that had actually weighed on his heart and lungs. The headstone was only two rows behind Kendra and Ariana's. It was made of white marble, just like Dumbledore's tomb, and this made it easy to read, as it seemed to shine in the dark. Harry did not need to kneel or even approach very close to it to make out the words engraved upon it. JAMES POTTER BORN 27 MARCH 1960 DIED 31 OCTOBER 1981 LILY POTTER BORN 30 JANUARY 1960 DIED 31 OCTOBER 1981 The last enemy that shall be destroyed is death. Harry read the words slowly, as though he would have only one chance to take in their meaning, and he read the last of them aloud. "'The last enemy that shall be destroyed is death'..." A horrible thought came to him, and with a kind of panic. "Isn't that a Death Eater idea? Why is that there?" "It doesn't mean defeating death in the way the Death Eaters mean it, Harry," said Hermione, her voice gentle. "It means... you know... living beyond death. Living after death." But they were not living, thought Harry. They were gone. The empty words could not disguise the fact that his parents' moldering remains lay beneath snow and stone, indifferent, unknowing. And tears came before he could stop them, boiling hot then instantly freezing on his face, and what was the point in wiping them off or pretending? He let them fall, his lips pressed hard together, looking down at the thick snow hiding from his eyes the place where the last of Lily and James lay, bones now, surely, or dust, not knowing or caring that their living son stood so near, his heart still beating, alive because of their sacrifice and close to wishing, at this moment, that he was sleeping under the snow with them. Hermione had taken his hand again and was gripping it tightly. He could not look at her, but returned the pressure, now taking deep, sharp gulps of the night air, trying to steady himself, trying to regain control. He should have brought something to give them, and he had not thought of it, and every plant in the graveyard was leafless and frozen. But Hermione raised her wand, moved it in a circle through the air, and a wreath of Christmas roses blossomed before them. Harry caught it and laid it on his parents' grave. As soon as he stood up he wanted to leave: He did not think he could stand another moment there. He put his arm around Hermione's shoulders, and she put hers around his waist, and they turned in silence and walked away through the snow, past Dumbledore's mother and sister, back toward the dark church and the out-of-sight kissing gate.
The fact that there is no Ron or Ginny around for what is the emotional apex of Harry’s journey in and of itself is revealing.
If it wasn’t meant to be a romantic scene, then JKR would have written Ron into the scene as well as, or instead of, Hermione.
If Ginny was with Harry in that scene instead of Hermione, Hinny shippers would be sobbing over how romantic that scene was (I would be too). There would be no question in anyone’s mind.
I don’t understand how so many people don’t see it—it’s only because it’s Hermione and not Ginny with Harry that some people don’t.
And then there is the nonsense argument that it’s a “sibling” relationship. Switch out Harry’s name for Ron, and Hermione’s for Ginny in the text, and then tell me it reads like a “sibling” relationship.
The intense emotional connection between them, the imagery and symbolism—including the arms around each other in a classic Couples’ pose and the “kissing gate” (yes—I know it technically has nothing to do with kissing. But JKR could have chosen to mention any style of gate, and that was the one her Muse went with)—was written to explicitly convey a romantic subtext, which JK Rowling herself acknowledged.
2008 I stared at her, sensing she wasn't finished, and a sense of foreboding crept in around the edges. "[Kloves] felt a certain pull between them at that point. And I think he's right. There are moments when [Harry and Hermione] touch, which are charged moments. One when she touches his hair as he sits on the hiltop reading about Dumbledore and Grindelwald, and [two] the moment when they walk out of the graveyard with their arms around each other." I was Holding my breath at this point. She wasn't done. "Now the fact is that Hermione shares moments with Harry that Ron will never be able to participate in. He walked out. She shared something very intense with Harry. "So I think it could have gone that way."