Why does tier Harribel hate Barragan?

Question

Even though she slashed one of his henchmen after refusing to join his crew in huecomundo. Even though i don't think this reason is strong enough for her to hate barragan. Where is the hate coming from?

Answer 1

this might stem from what was shown in what the Wiki refers to as the Anime Only Content from the Fake Karakura Town arc

Apacci asked her why [Tier] should allow [A Hollow] to escape instead of devouring him. Explaining the law of Las Noches, she asked Harribel why she does not follow it. Stating she did not want to become stronger by devouring and sacrificing others, Harribel resolved if she could not win alone, she would win in a group. At some point, Harribel and her group came face to face with the King of Hueco Mundo, Baraggan Louisenbairn, and his court. The two revealed they had previous dealings with each other, and Baraggan, noting he was tired of her rebellious attitude, gave her a choice: she could either join his army or run off to an area he could not see, noting there is no place in Las Noches he could not see.

Source: Tier Harribel > History > Fake Karakura Town arc (anime only)

now there's a couple of things to unpack here.

first off she's had dealings with Baraggan before but we don't know what they are, but given how Baraggan find her rebellious and wanted her to join his army (implying to fall in line) or to go somewhere he wont see/be troubled by her might suggest that Harribel and Baraggan are at odds with one another.

another thing is also what Apacci said is the "law of Las Noches" being to devour one another which is at odds with Harribel's personality

She strongly opposes the notion of killing others, especially if done to gain power

Source: Tier Harribel > Personality

and given that Baraggan is the King of Las Noches one could infer that this "law" is something he started where he seeing her as rebellious because of her personality being something opposite to the law of Las Noches

however the wiki does say that this part of Harribel's past is anime only and the Wiki states that it does not constitute canon material.

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Aside from what we see of her past in the anime, another point to consider is her personality in not only how she opposes killing others but also how much she cares for her Fracción. while Barraggan was about to have his army slaughter one another out of his own boredom

(To Sōsuke Aizen, Gin Ichimaru, and Kaname Tōsen) "I was just beginning to succumb to boredom. Had you not appeared here today, I might have divided my own army in two and had them slaughter among themselves."

Source: Baraggan Louisenbairn > Quotes (11th point), also from the manga; Chapter 371, page 6

whether Harribel knew this or not can be debated but it shows the kind of person Baraggan is and is someone that she would dislike at a personal level