This answer is a little bit "meta" as regards the story.
A way to understand Robin's (Meagan's) uses of the Wit as major theme in the Fitz stories (I have read them all, and am now enjoying the Fool trilogy's second book) is to look at allegory or "the bigger message" themes embedded in her writing. She writes with a lot of layers of complexity and meaning, which is a reason I enjoy her books so much.
On her sff.net home page discussion board, over ten years ago, Robin shared an insight (may also have been shared in an interview) about the Skill along the lines of her story question for the Farseer Trilogy: "What if magic was addictive?" She used that as a jumping off point in her world building for the Six Duchies to see what toll was exacted on users of magic. The price Prince Verity pays for his use of the Skill is an interesting description of a someone addicted as seen through eyes of someone (Fitz) who loves him. Learning that from her changed how I saw the Skill in her stories. It got me looking at other larger themes. (No digressions to Liveship Traders).
The King as Sacrifice:
Robin shared on that same discussion board, during a thread that rambled into how people were or weren't tolerant of homosexuals, that she was born and raised Catholic. (The rest is off topic, so I won't digress beyond remembering her PoV as being about opening our hearts to those we know and those we meet). As soon as I learned that last about her background, I "got" her Big Theme treatment of the Mountain Kingdom culture and Princess / Queen Ketricken. Catholic theology makes a big deal of Jesus as King, Jesus as High Priest, and Jesus as Sacrifice. What Robin did was apply that last theme, and folded it into a mortal kingdom: how would a royal family behave if they tried to "be Jesus" to their people, to be their Sacrifice, to be their servant? (There are numerous tropes about benevolent kings/sovereigns in Western literature ... many of which find their ways into fantasy and Swords/Sorcery stories as tropes). With that insight, how the social structure of the Mountain Kingdom comes across changed the story for me, and made me appreciate the characterization of Ketricken even more. (She was a favorite of mine from the get go).
As a theme, it's a metaphor (or used in allegory) dealing with prejudice and bigotry. You can see in it very familiar themes of "burn the witch" and about how different/strange/the other people are treated in a given society. (Robin explores similar themes in the Soldier's Son books, but that's off topic).
You first see this play out in a Large Theme sense when you read Assassin's Quest, then much more in the Tawny Man trilogy.
Before Fitz meets Black Rolf, the Wit is this "thing" that Fitz and Burrich deal with, and of course use to get Fitz out of town/prison. Fitz feels very much the outsider for a lot of reasons, but one of them is society's attitudes. He may be of royal blood, but he knows he's not welcome as he truly is, and not just because he's a bastard.
He almost goes feral after the jail break, so he at least finally comes to terms with himself.
When Fitz encounters Black Rolf (man and bear bond) whose wife has a lady and bird bond, he finds them comfortable with their unusual trait, but all isn't happy. They live as "outsiders." (The other side of the tracks, the (insert minority) side of town.)
(Aside: While I saw this as an off angle look at being 'in the closet' that may be me reading too much into what she was writing. It may have been gender or racial discrimination/bigotry from RL being used as a model).
They are ostracized from society. Fitz' meeting them shows you their humanity through his eyes, so that you the reader get past that 'other' boundary that people in the story can't seem to. (Quick cut scene to Martin Luther King and "Content of our Character" in his "I have a Dream Speech.")
During the course of the Tawny Man books, Fitz is a champion for the cause of the witted, but he has to work within the system. He addresses a Royal with "tainted blood" in a society bigoted against him. Wait a sec: JFK was born and raised Catholic. That was for some grounds to not vote for him. "What, can a Catholic be a President?" (In 1960, this was an affront to WASP society -- yes, I am that old).
The Wit is a vehicle that Robin uses in part to enchant us with a magical tale, to provide internal monologue for Fitz/Nighteyes, but also to address prejudice and bigotry being deeply ingrained in a culture.
To answer your question:
Why is the Wit a source of such hatred and powerful emotion?
There's more to it than just in-story elements. It's a way to explore human behavior that still persists: intolerance and bigotry. Part of what makes Fitz and his friends heroic is their effort to change this long standing prejudice in the story that had lasted for centuries in the Six Duchies. This is a form of conflict resolution for the story, and perhaps is offered as a model for any reader for their own lives in dealing with mundane reality, warts and all ... which includes dealing with bigotry.
Fitz, as Mal Reynolds might say, really is a big damned hero, even if reluctantly, and not just because he kills bad guys.