Note: I do not claim to be an expert on the subject. But these are my educated observations.
This song is very popular internationally which is interesting as the song is basically describing an extremely abusive relationship. How common is this that people aren't repulsed by this description but instead embrace it as their own? How many have faced this, wither directly by way of being the abuser/abused, or indirectly by way being close to a person involved or even a child?
The perverted male protective instinct presented in the song. The male talks about how much he loves the woman and hates it when he is violent and she leaves. When the man is not taught to protect then the instinct is perverted into control or to abandon, and control is what happens in this case. There's also an issue with drinking and anger, but that's another issue.
The woman ultimately wants that companionship so she will subject to it. Despite the violence she feels safe with him because what she wants is safety, aka protection. It is very common for those that are abused to return to abusers despite even a threat to death because of this safety.
There's a lot of pain in this type of situation. The man fears the woman will leave, and the woman fears what will happen if she leaves the man. Fear is what drives this. A fear that they can't get any better, fear of losing the "only person that has ever truly loved them". There's also masochistic behavior based on a lie that they deserve what they get. There also can be an element where physical behavior connects them in a way where they become emotionally bound to each other.
The solutions to this are inner healing that only God can bring. Change can come in time but that requires recognizing the problem and getting to the root, something that is very painful and is usually generational.
In the bigger picture it would be easier to have preventative counseling before the relationship gets to this point but that usually only happens in premarital counseling. As situations like this are more common amongst those that live together that seems unlikely.