These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Bastard Boyfriend: Honestly, this troper—as someone who very rarely reads shojo, specifically because of this trope—was pleasantly surprised when he actually tried this manga. YMMV indeed, but I feel like this manga gets a bad rap due to the BDSM flavor to the art. In reality, the relationship between the leads is mutual, and loving. While Kyo is doubtlessly a bit of a pervert, his temper and teasing always remains well within the bounds of what would be considered acceptable within real-life relationships; to say nothing of where that puts him in relationship to the vast host of genuinely abusive shojou "heroes".
Complete Monster: Kuzonoha Shuuhei. While all the male characters in Black Bird are a bunch of misogynist jerks, Shuuhei stands out among the whole bunch as the most cruel and depraved. Following a failed attempt to rape Misao, he severely wounds her to facilitate her abduction from Kyo's dojo. By his own admission, he has no qualms about injuring her as long as she is able to provide him with an heir that will consolidate his position as the head of his clan. Only a total bastard like this can make Kyo seem like a knight in shining armor to Misao by comparison.
YMMV here; cheesecake cover-art aside, there's very few instances of anything that could be realistically called "abuse" within the manga, and the instances that do occur are perpetrated by villanous characters and portrayed as wrong. Sexy—BDSM themes are obviously present in the manga, after all—but wrong.
When a certain Jerk Ass Kyo's brother Sojo ties our heroine up, encases her behind a magic barrier, and then when Kyo breaks through, starts talking about how great it would be to rape, kill, and eat Misao in front of him (not even necessarily in that order!).