"Their very nature violates the most core of Noxian principles. That every one of us is equal on the battlefield."
Ambessa says those words to Mel after her daughter offered to return with her to Noxus. The most common interpretation of that scene and, that quote in particular that I've seen, is that Ambessa hates mages because they have an 'unfair' advantage on the battlefield (or something along those lines) If that were true, her willingness to use magic for her own gain, would, of course, make her a hyprocrite.
I think there is actually a more complex undertanding of honor behind her words. That doesn't necessary make her a better person but certainly a less ignorant one.
Ambessa has followed the Medarda code her entire life. One maxim of said code is: "A Medarda fights with honor"
The first scene we have with Ambessa shows her killing a unarmed prisoner. Not an honerable fight by any means, but I don't think that's what honor means to Ambessa.
"I haven't. Everyone else has just gotten faster. And they're cheating. It's not enough to win-"
"It's how you win. I know."
That's a conversation between Ambessa and her grandfather, which, on first glance, is pretty confusing. At this point in the book it has already been implied that both of those people have sacrificed family members for the sake of victory. What could an honorable fight be to them ?
"Is that when you stopped respecting him? She thought to herself. When he lost the taste for blood?"
This quote is about Ambessa's cousin Ta'Fik who is at war with her. Ta'Fik is very determined to defeat Ambessa and is willing to kill people close to Ambessa (Mel, Kino and her husband Azizi) to get to her. Still, Ambessa believes that he lost his taste for blood (which is obviously a bad thing in this context), because he doesn't lead his own warbands anymore. Instead, he sends his daughter to fight Ambessa.
I think that's something that Ambessa finds dishonorable: leaving the fight to someone else, or even just striking from a safe distance. (Technically, there is also a scene were someone tries to stab Ambessa while she has her back turned. That is also considered a big no-go by multiple people in that scene, but Ambessa herself seems more mad that Ta'Fik sends someone else to kill her)
"You will shed the blood of others, but what of yours-your own-your heart-will you sacrifice ?"
Ambessa is asked that question in her death vision that she has while pregnant with Mel. We know from Arcane and her music video that the answer to that question is yes, Ambessa is very much willing to sacrifice. The lamb she lets go of is a part of her (it's not Mel or Kino) and she has to give it up willingly in order to pass her trial. Even before that, Ambessa is brought up in a way that teaches her that enduring pain makes you strong and that dying in battle is an honerable thing to do.
Here we have a person who believes that you should not play it safe and that an honorable fight is a fight in which you have something to lose too (your life in most cases). That doesn't mean a physical fight has to be even. It just means there's always a (calculated) risk that she is willing to take.
Now, what does that have to do with magic?
First of all, Amnbessa doesn't seem particularly anti-magic in the book.
"She looked above, as if she could see what was to come in the lines of the stars. Some mages were said to do that. She wondered if Rudo could, with his celestial magic, but she decided it was better not to know."
To some degree (and mostly when it comes to Rudo and Mel) I would say that she finds it quite beautiful even, while still not feeling completely comfortable with it (e.g. choosing not to ask Rudo about his magic.) She is very eager for Rell to fight with magic and sees it as a tool for power, but she still wants Rell on the battlefield, fighting according to the Medarda's idea of an honorable fight.
"At least I do it with my own bare hands, my own power-"
This is a conversation between Rudo and Ambessa, where Ambessa expresses disdain for how the black rose works (especially the kidnapping young mages thing). Rudo tells Ambessa that it's no different than what Ambessa does (I assume that was supposed to refer to Rell who Ambessa takes in as a trainee). The interesting part about the quote is that Ambessa doesn't seem to understand magic as part of the mage. I do think that there is a disconnect there and that fighting with your own hands would seem more 'real' to her than fighting with magic, but it's not a general dislike for mages.
"For the sick sense that she was grateful Mel had never shown any inkling of magic, lest she share Rell's fate. For the guilt that she still wished Mel had power, so that she could be greater, so that they could be greater together."
In my opinion, the book did a very good job in tracing everything Ambessa endures back to the black rose in one way or another. She makes her own bad choices that cause her pain, but the black rose is looming over her for the entirety of the book. It explains why she is the way she is in Arcane. It makes sense that she dislikes the black rose for what they did to her and it makes sense for her to hate the way they fight because her character has a very specific idea of what honor is.
A mage who works with illusions and hides in the shadows goes against everything she believes and in Arcane we see Ambessa stick to her beliefs for better or worse, until it kills her. She hates the black rose for a very specific set of reasons and not out of a general fear a inferiority when it comes to mages.
And she certainly doesn't hate Mel because she is mage.