Harry does not walk all over her, he just has a temper. Hermione tolerates it because his anger is almost always valid. He doesn’t let out his anger to be dickhead, it’s called venting your emotions.
When you’ve realised Voldemort has returned, and no one is telling you anything and no one believes you and you’ve just been tortured and almost killed by Voldemort and stuck with no one but your shitty relatives your whole summer while your friends are all having fun together, a fifteen year old isn’t gonna be keeping in their emotions and remaining all calm and composed.
And it wasn’t just about the stupid firebolt, Ron had just seen his rat all bloody on his bed and Crookshanks has been tryna attack for the past few months, so naturally everyone thinks the cats killed him and Hermione continued to defend it. Given that the evidence was right in front of them, they can’t be blamed for thinking the cats killed Scabbers nor can they be blamed for being mad at Hermione continuing to defend the cat they thinks killed their rat. They don’t know about Peter yet so that doesn’t matter.
And Harry was having a very tiresome year, and Quidditch is one of the few things that brings him joy and he lost his broom in the last match due to a dementor attack. And Hermione, without even consulting Harry, tells Professor McGonagall. Well-intentioned or not, having someone meddle in your business without your permission and have the choice taken away like that would annoy anyone. Also, they’re all literally thirteen in this and he’s got this brand new amazing broom, and it gets taken away because Hermione meddled when it wasn’t her business to do so. Whether it’s for safety or not, Hermione has no right to make decisions for people. That’s literally one of her main flaws, she’s meddling and controlling. Coming from someone who grew up with controlling parents.
If Hermione had simply talked to Harry first, no one would be mad at anyone. It’s the fact that she interfered with someone else’s business. Plus he’s literally on the Quidditch team, his team relies on him, he needs to practice.
And her breaking the wand, trying to say Hermione was wrong to be apologetic - HELLO??? THEY’RE IN THE MIDDLE OF A WAR AND THE WANDMAKER HAS BEEN KIDNAPPED SO HE CAN’T GET ANOTHER ONE AND BASICALLY HAS NO MEANS OF DEFENDING HIMSELF and that wand has been by Harry’s side from the very beginning so naturally it holds sentimental value and was his only protection. So naturally Hermione is wary that Harry is angry. Because despite that it was accidental and that Hermione saved him, it is still pretty bad that Harry now doesn’t have a wand at a time like this.
Hermione knows Harry’s life is a constant cycle of trauma and loss so she knows it isn’t fair to come down on him for his anger. And Harry knows Hermione can be meddling, controlling and stubborn and he puts up with that.
It appears Hermione has more empathy as a kid than most of the older people who post about these books.
Seeing as this person is a Romione shipper, I think the bigger concern is that one needs to put down another ship to make theirs look good, you’d think a ship actually worth its salt would have enough sustenance to shine on its own.