Why if a child doing bad things they put the fault or blame on the child's parents?

How stupid and irrelevance of that. Yes, they nurture the child since childhood but when the child is adult, it is already out of their hands to control their kid.

I hate when elders blaming the parents because of the sins that was made by the child.

I do sins. Blame on me, shame on me. Not them. They have nothing to do with my deeds.

They aren't perfect but ain't bad either. The world is not about black and white. There is grey lies between it.