The "crazy/terrible girlfriend" trope appears everywhere, including anime; while certainly an overused, and many times sexist, descriptor, such a characterization does feel appropriate when describing the worst anime girlfriends of all time. Given the number of dysfunctional anime relationships out there, it stands to reason a few terrible anime girlfriends are a part of them. While everyone follows different criteria for what they want from a partner, most agree that a few things are of critical importance when it comes to showing basic respect for your partner as a human being. Not manipulating them into doing things they don't want to do. Not cheating on them. Not stalking or assaulting them. Not murdering them.
This an an extremely low bar, but sadly, there are plenty of anime girlfriends who can't manage even that much. Some are murderous stalkers like Yuno Gasai, and others are prone to physical violence like Naru Narusegawa. No matter how cute they appear, you definitely would not want any of these ladies as your girlfriend or your wife. That said, don't think that anime only makes the ladies look bad: plenty of boring anime men out there make for equally terrible boyfriends, and honestly, they're probably the reason why all these anime girlfriends are acting out.
Akane Minagawa puts up on the appearance of being a good girlfriend, but it is an appearance only. This seemingly mild-mannered music teacher feels no genuine love for others. To deal with this, she sleeps with everyone from random dudes she meets to one of her underage students. She does all this while she's dating a fellow teacher, the actually kind Narumi Kanai – a relationship she gleefully rubs in the face of another student, who she knows is in love with Narumi.
Cheating on your boyfriend is bad enough, but cheating on him via criminal activity is even worse. While Akane eventually decides to give up on her dishonest ways and marry Narumi, she still spends a ton of time lying her face off and being needlessly cruel. There's no reason to assume such behavior wouldn't carry on into the marriage.
Terrible qualities aside, Sola-Ui Nuada-Re Sophia-Ri would be difficult to date – after all, who can remember that name? As it were, her name is one of the least difficult things about this girlfriend – sorry, fiancée.
She hates her chosen partner, Kayneth El-Melloi Archibald, from the start. Though acrimony towards arranged marriages is a totally understandable response, Sola-Ui unfairly takes it out against the one person, Kayneth, who had just as little say in the matter as her. She constantly criticizes Kayneth in front of his colleagues and superiors and never takes his side on any issue, no matter what it is.
Kayneth's own Servant, Lancer, becomes an object of Sola-Ui's affection, who starts slowly falling in love with him. When Kayneth ends up bedridden with severe injuries, Sola-Ui tortures him into relinquishing his magical bond with Lancer and transfer it to her. Yikes.
Benten never officially starts dating Yasaburo, but she does spend the entire series flirting with him. In doing so, she makes it super clear she would suck at the whole girlfriend thing. Yasaburo is willing to accept basically anything Benten does because he finds her attractive – meaning he overlooks her participation in a ritual that involved killing and eating his father.
But while Benten more than happily accepts Yasaburo's misguided affection for her when convenient, she also totally disrespects him, expecting him to do whatever she asks at the drop of a hat. This is because she was raised as a tengu, a species seen as superior to Yasaburo's shape-shifting species, the tanuki, in the world of The Eccentric Family. This dynamic more or less forces Yasaburo to accept that Benten killed and ate his dad, and why he's expected to be subservient to her in their budding relationship.
When he ultimately decides instead to marry Kaisei – another tanuki who his family arranged for him to be with – instead of Benten, it's a relief for many viewers.
If you stab your boyfriend to death and then chop off his head, you likely will not win the title of Girlfriend of the Year. No matter how terrible your boyfriend is, short of him threatening your life, murdering him is an excruciatingly bad way to deal with your problems. Sekai Saionji's boyfriend Makoto Itou does cheat on her multiple times, but Sekai also got with Makoto while he dated Kotonoha Katsura the first time. She could probably have predicted that he'd cheat on her too.
Even if she didn't, the appropriate response would be having a mature conversation about her issues – or yelling at him, breaking up with him, maybe even embarrassing him by telling his grandma all the salacious details – not beheading him.