It is because children are too easily influenced that they need access to the unrestricted internet. To pick what is perhaps a trite example at this point - yet very real - a child experiencing same-sex attraction can be easily influenced by their parents, who they spend most of their lives with, to believe that such a thing is unnatural and best off suppressed. Access to the internet cam show them that there is a very large community of people who disagree with that viewpoint.

Or, more broadly, consider how historically common it is to choose the same profession as a parent. Access to the unrestricted internet can let you discover fields that may not have even existed when your parents were in college and even try them out (see also https://xkcd.com/519/).

If we had stronger cultural norms of collectively raising children in the village (the whole village, not just a church of specific beliefs and traditions that attracts the like-minded), this argument wouldn't be as strong, but we don't.