Parents taking responsibility for raising their children is not the "Big Brother" position here. That designation properly belongs to those who advocate intrusive government meddling in the private affairs of the adult citizenry.
You are correct, in the Orewellean sense, Big Brother refers to the personification of the power of the state in the movie 1984.
Since then, it had morphed into "an all-powerful government or organization monitoring and directing people's actions", which is currently used to personify the fears of the people that the goverment is becoming too involved in their lives.
Although, we have not quite arrived at the Orewellian defintion, it is still used as an association none the less.
Fortunately, utilizing my, also great, powers of association I choose this image to successfully (my definition) illustrate my point.
I am a strict advocate of parental responsibility. I also know what micro-management does to a persons ability to make rational decisions.
So where is the balance? Would you have parents micro-manage their children to the point where they are incapable of making decisions? Or would you create an enviroment where parents can foster decision making ability based on their own belief system? Or would you choose to impose your beliefs and values on them at an impressionable age.
Yes, parents are responsible to protect and nuture their children, but nobody can control their environment, it's outside their "sphere of control".
This is where you and I can help, as a whole we have the ability to influence the environment, to make it a little easier for parents to raise their children without being buffeted by the vice-mongers.
We need to allow the children to learn how to make decisions before we expose them to the harshness of life. Protect them until their old enough to make those decisions on their own.
Let's keep the door locked for now.
For what it's worth, that's my 2 cents.