So true. Parents and children can be narcissists. However if I read from parents that they have done "nothing wrong" it is a red flag immediately. I have two young kids. Being a good parent is hard.
We all make mistakes all the time and the important part is to make good for them and not reject all responsibility for problems that have emerged.
If your child rejects you, maybe you should not go and demand proof of your wrongdoing. Sometimes even you must acknowledge failure if you are convinced otherwise because you are the parent and have to be an example.