No, the burden of proof is on those who seek to diminish the right.
Until people understand the proper way to argue this point, the courts will be free to do what they want. There is a presumption of fitness for both parents. You can hold a judges feet to the fire on this. These days, however, it may take an appeal. Is it worth it? I think it is.
Understand that but the presumption of fitness does not always extend to the father.