Of course you can have an unhealthy attachment to your child.
You can take an anxious child and, out of love, accidentally help them avoid all scary things and think your major role is about protecting your child. This will make their anxiety worse. That is the case for very small children, but your role as a parent is to set them off to live their own lives. That is an unhealthy type of attachment.
You can believe that your child can do no wrong and is the most marvellous creature in the universe. I don't mean feel they they are in the way nature programmes us to, but know they aren't really, I mean genuinely believe that they are. You can indulge every whim and buy every item for fear of your child's upset and make them believe they are the centre of the universe. That is an unhealthy type of attachment.
You can believe your child is bad and try desperately to "save" them by beating the devil out of them. That is an unhealthy attachment.
You can make your child feel guilty for wanting to separate from you and forge their own life, cling on to them, and that's unhealthy too.
There are so many ways it's possible to have an unhealthy relationship dynamic with ones children, including when adult.
As Philip Larkin said, "They fuck you up, your mum and dad. They may not mean to, but they do".
Which doesn't mean they shoulder the blame for what their daughter did btw!