There's nothing wrong with depicting unhealthy relationships in media - as long as you acknowledge that they're unhealthy. If you frame the unhealthy relationship as, in fact, being unhealthy, and that relationship is dealt with with that in mind, I say go for it!
Most of us realise that there's a difference between fiction and reality - but when a vast majority of stories, or when one super popular story, depict very unhealthy relationships as something positive, admirable and worthy of striving for, that's problematic.
Take Twilight as an example. Never mind the quality of the writing or the clichés about vampires or the sparkles - just focus on the ideal it presents to the readers. Bella falls head over heels in love with Edward - who despite the sparkles is very literally dangerous - and he then invades her privacy by breaking into her bedroom at night (we're told this is supposed to be romantic), dismisses her feelings and makes decisions for her (he dumps her "for her own good", leaves without explanations), and puts her at risk by doing so. She, on the other hand, loses all sense of self-preservation, hurts the people who love her (she ignores/doesn't explain things to her father, who obviously cares for her), and repeatedly puts herself in mortal danger just so she can receive visions of her lost boyfriend. She also emotionally manipulates other characters into doing things for her, because she's so monomaniacal when it comes to Edward that she loses sight of all else.
This presents codepencency, self-harm, outright suicide attempts, gross invasions of privacy and emotional manipulations as romantic ideals. I know they're not something to strive for, but put that book in the hands of a very young girl or boy who doesn't know, and they might gain a skewed notion of what they should expect out of a relationship.
Now, if it was just one story doing this, we could maybe shrug it off - but these romanticized versions of emotionally unhealthy or even abusive relationships are everywhere in media, which makes them something to be concerned about. It is alarmingly common to see romance-stories framing rejections as just an invitation to try again and again until the intended target for affection gives in - even though in real life, that would qualify as stalking at best.
The culture and media we're exposed to does influence the way we think about things, perhaps more than you think. It's why propaganda works.