Sure, just like the kid needs the keys to the car or the liquor cabinet. On the other hand, kids need to learn to drive and to drink (if at all) responsibly. That said, two cautionary tales of our times:
A chilling recent story in Ars Technica recounts:

On November 10, a 12-year-old girl left her home in the Baltimore suburb of Nottingham at 7:30am, heading to her middle school. She never returned home. When her mother called the school later, she discovered that her daughter had not even arrived. Suddenly, Baltimore County Police were calling in the FBI to assist in their search for a missing person.

According to police reports, “an unfamiliar blue pick-up truck with North Carolina license plates” was spotted by neighbors near Jane Doe’s home that morning. (While the girl’s name was previously published in Baltimore local media, we’ll refer to her by the name used in recent court documents—Jane Doe—because of her age and because of the nature of the crime allegedly committed against her.) Over the next four days, the investigation of Jane Doe’s disappearance led to a ranch house on a cul-de-sac 340 miles away in Raleigh, North Carolina. That’s where North Carolina Alcohol Law Enforcement agents working under the direction of the FBI eventually found the kidnapped girl—along with a 32-year-old probationer named Victor Yanez Arroyo.

The girl is now back with her family, but according to arrest documents, Jane Doe told authorities that “at the residence, Arroyo had non-consensual sex with her two times.” Arroyo was arrested and now faces a wave of state and federal charges.

Tracing her digital trail, police found her alive.
Scariest line from the resulting transcript:

[Other user] did u tell your mom?

[Jane Doe] no because I used kik and I’m not supposed to have it so Id get in big trouble.

Yes. Trouble even her mom couldn’t get her out of. Maybe the police couldn’t have either.
Then there is “Police rescue teen abducted by Facebook ‘friend’ Karachi, 2013).
According to the vid from San Diego police below, one in 25 American teens receives a sexual solicitation online. Most such invites probably fall into the void unheeded by recipients. But the few that don’t can spell big trouble.
An underlying problem may be that busy and distracted parents assume that what happens online is trapped in the bubble of a digital world. Yet in certain ways, the Internet is even more dangerous than the mall. That is because a user can, over time, build a persona at odds with reality.
The cool character we think we are communicating with on the other side of the world may in fact be on the other side of the street. We may think he is sixteen and in school; he may in fact be thirty-seven and violating parole.
About the baby on Facebook: I thought I’d seen everything, but then my editor sent me this:

Plush dolls made for infants will let them engage the social age

Essentially, playing with the soft toy automatically produces Facebook images:

In the collection is a a crib mobile equipped with a motion-sensing camera that automatically captures videos when the baby reaches upwards.

Another camera is attached to the side of the crib. By rolling a ball, the device will start taking photos and uploading them to social media paired with randomly selected captions with hashtags such as “Taking pictures in the crib!! #myfirstselfie.”

“I thought it was weird to be involved in the life of someone who doesn’t even know that I have seen everything in his life already,” [developer] Cornet tells Dezeen. “And the baby couldn’t make a choice to maybe not show me.”

“Weird” is one way of putting it. “Thoughtless” is the one that came to mind.
In theory, such social media groups can be private. In practice, why risk it? There is hardly a shortage of ways to keep in touch with those who have a legitimate interest in the latest addition to the family—ways that entail far less risk than random use of social media.
Teens need to learn that the Internet is a public space like any another. It isn’t somehow safe just because contacts are made online. See also: Are Facebook friends replacing real friends?
and Fake Facebook accounts Next: Is spying on one’s kids, using new software, the best way to keep them safe?
Advice from rescued teens and the police:

Denyse O’Leary is a Canadian journalist, author, and blogger.