"The bottom line is, it's the best and the worst of the world. It makes good people able to spread good messages and constructive messages further, and it lets bad people find each other and do bad things," he said.
"In some cases it's bullying, in some cases it's underage sex, as you described - the internet encourages the best and the worst. It's not all a good thing."
Despite the dangers, parents are still keen for their children to embrace the internet.
When the World Internet Project started 13 years ago, 98 per cent of parents said there was "bad stuff" online, Dr Cole said.
"Of course they were right, but 97 per cent of parents said it was essential that their children learn how to use the internet.
"Normally you wouldn't let your kids near anything that had so much bad stuff."
Dr Cole said parents had always taught children basic safety, such as looking both ways before crossing the street, but they now needed to teach them internet safety as well.
"One of the new rules is `don't assume you have any privacy - don't assume that anything that involves more than two people is off the record'."
Dr Cole cited the new "revenge porn law" in his home state of California as an example of a law change to tackle the internet's bad side.
So-called revenge porn involves people sharing explicit images or videos of their former partners after a break-up.
The new law, signed by California's governor last month, makes it illegal to share such content without consent - but only if the images or videos were taken by the person who posted them online, rather than by the victim themselves.
Dr Cole said such laws aimed to prevent "the incident that just happened" rather than new developments.
"Most people trying to stop something are fighting the last war, and we're not looking at much anticipating what could be happening," he said.
"That's human nature - it's not a criticism of police, that's not a criticism of authority. That's just pretty much the way we work, pretty much the way parents work, as well. You punish kids for what they do, and of course you can't punish them prospectively."
New Zealand's cyber bullying bill, introduced by Justice Minister Judith Collins, would make it an offence to send messages and post material online with the intent to cause harm.
The maximum sentence for the offence would be up to three months in prison or a $2000 fine.
The bill would also create a new a new civil enforcement regime with an agency that would be the first port of call for complaints.
People would be able to quickly and easily request the removal of harmful content from websites, while serious complaints could be taken to the district courts, which could issue take-down orders and cease-and-desist notices.
The bill would also create a new offence of incitement to commit suicide, even in situations when a person did not attempt to take their own life, which would be punishable by up to three years imprisonment.