What is the significance of Kat's despising of Hemingway?

Kat's exact quote in the film was in response to a fellow classmate calling Hemingway a romantic:

Romantic? Hemingway? He was an abusive, alcoholic misogynist who squandered half his life...hanging around Picasso trying to nail his leftovers.

Let's break down Kat's accusations of Hemingway:

• Abusive - Hemingway was mentally abusive to each of his four wives and many lovers. He was famous for his volatile temper. There is no definitive evidence that Hemingway physically abused his many lovers, but he did make a lot of them suffer mental abuse.
• Alcoholic - Hemingway was a heavy drinker for the majority of his life.

• Misogynist - Hemingway was definitely a "man's man" and had somewhat of a controversial view of women. For example, there is a passage from a letter that he wrote to his editor, Maxwell Perkins in 1943:

  A woman ruined Scott [Fitzgerald]. It wasn’t just Scott ruining himself. But why couldn’t he have told her to go to hell? Because she was sick. It’s being sick makes them act so bloody awful usually and it’s because they’re sick you can’t treat them as you should. The first great gift for a man is to be healthy and the second, maybe greater, is to fall [in] with healthy women. You can always trade one healthy woman in on another. But start with a sick woman and see where you get. Sick in the head or sick anywhere. But sick anywhere and in a little while they are sick in the head. If they locked up all the women who were crazy — but why speculate — I’ve known goddamned good ones; but take as good a woman as Pauline — a hell of a wonderful woman — and once she turns mean. Although, of course, it is your own actions that turn her mean. Mine I mean. Not yours. Anyway let’s leave the subject. If you leave a woman, though, you probably ought to shoot her. It would save enough trouble in the end even if they hanged you.

  Hemingway was an avid boxer, big game hunter, fisherman and outdoorsman.

• Nailing Picasso's leftovers - Picasso and Hemingway were acquainted in Paris and were introduced to eachother by Art enthusiast Gertrude Stein in the 1920's. Both were ego maniacs and womanizers. It is always just assumed that Hemingway and Picasso competed with each other for women because they competed with each other in every other way. There is a woman named Sara Murphy who both Picasso and Hemingway claimed as a muse.

Kat also despises Hemingway because she is seen as a passionate feminist who stands against all of the male stereotypes which Hemingway represents.

She would rather read literature by female writers. She suggests to Mr. Morgan that the class read works by female authors:

What about Sylvia Plath...or Charlotte Bronte or Simone de Beauvoir?

Why?...she says why...she disapproves of him as a person.

Hemingway?! He was an abusive alcoholic misogynist who squandered half his life hanging around Picasso trying to nail his leftovers.

As for racism, the teacher doesn't actually accuse her of that; it's more about the fact that, in his eyes, she's protesting about the wrong things.

Transcript

MR. MORGAN: And Kat. I want to thank you for your point of view.

She smiles to herself, her social indignation justified.

MR. MORGAN (continuing) I know how difficult it must be for you to overcome all those years of upper middle class suburban oppression. It must be tough.

She deflates and becomes bitter again.

MR. MORGAN (continuing) But the next time you storm around the PTA crusading for better lunch meat, or whatever it is you white girls complain about, ask them why they can’t buy a book written by a black man!

She explained it herself:

Romantic? Hemingway? He was an abusive, alcoholic misogynist who squandered half of his life hanging around Picasso trying to nail his leftovers.

I believe that for the rebellious, feminist-oriented Kat the fact that he was a mysogynist was the most important. Whether this is true is a different story, you can see this Quora discussion for more information on the subject.

I believe the implication of that scene was that she was transferring her dislike for what one particular guy did to her years prior onto guys in general, using Feminist language. She saw Hemingway as an exemplar of that kind of guy.

The teacher likely felt unfairly personally attacked by this (being both a guy, and in fact the guy who assigned this particular writer), and decided to give her a taste of her own medicine. As an African-American talking to a very privileged white person, race is what he had to work with. Was it unfair and unreasonable? Probably. But so was dumping on him (and disrupting class) because some other guy got her drunk during her freshman year.