This is a gray area that I doubt will ever be brought to any sort of resolution that makes everyone happy. All in all, I believe that yes, parents should be held responsible…in certain conditions.
As with nearly everything today, there is really no black and white, but graduated shades of gray that must be delved through. Children are the product of their environment. Genetics have some bearing, but the environment is key. This is shown over and over again in adopted children. If a child is engaging in criminal behavior, then to determine if the parents should be punished the law needs to look at them on a case by case basis.
Are the parents neglectful? Do they leave the child alone for long hours, and I am not talking about work hours. Work is one thing, traipsing off to drink a few beers is quite another.
Is there abuse in the home? Is the child being abused in some way shape or form so that the only way they can act out their confused emotions is through criminal behavior? This is another factor that should determine whether parents should be held accountable.
If the parents are doing nothing to stop the behavior in question, and in fact are defending it for whatever reason, then yes, they should be held accountable for the child’s actions. After all, it is all the child knows in a case such as this.
However, if a child is being raised by parents that are doing all they can to get this child help, regardless of their financial situation, who do not abuse the child and give the child what they need in the way of emotional support, then the child should be held accountable for their own actions. Parents can only do so much. Only so much discipline, so much love, so much support can be given before something must break. Often times, it is the child that must be told that they will be held responsible for their own actions, and perhaps this will curtail the behavior. If not, then the child will see only that they are not held responsible, that they can get away with whatever they want, and it will continue.