At the end of the film The Social Network, Mark Zuckerberg approaches the ex-girlfriend whom, earlier in the film, he had dragged through the mud online. He wasn’t getting her back, of course. As she put it: “The Internet isn’t written in pencil, Mark. It’s written in ink.”

But what if that could change?

A growing group of privacy advocates in the U.S. and abroad want the Internet to be written in pencil. In particular, they’d like it to be easier for their children to take down posts or other information that they once put online and now wish they hadn’t.

The movement is particularly strong in Europe. The European Union, which proposed legislation on the subject last year, calls it the “Right to Be Forgotten.” The 20-page document proposing the legislation advocated sweeping changes to privacy online, according to the U.K.’s Telegraph. Individuals could sue websites and delete just about any information about themselves online. Internet users would have to opt in before companies could track their data in the first place. “The protection of personal data is a fundamental right,” explained Viviane Reding, the EU commissioner for justice in charge of the proposed rules.

On Wednesday, news emerged from Spain that the “Right to Be Forgotten” was being taken very seriously there indeed. The Associated Press reported that Spain’s Data Protection Agency ordered Google to remove links to material related to about 90 people. These include plastic surgeon Hugo Guidotti, a high-ranked Google hit for whom is a 1991 newspaper story about a $7.2 million lawsuit on a breast job that allegedly went bad (Guidotti eventually won the suit). Hardly good for business.

“This is just the beginning, this right to be forgotten, but it’s going to be much more important in the future,” said Artemi Rallo, the Spanish Data Protection Agency’s director, according to the AP.

It’s likely to become more important in the U.S. as well, if American activists have their way. Last December, an online-safety organization called Common Sense Media argued that “Web companies should develop tools that make it easier for young people—or their parents—to completely opt out and delete this information.” They wanted, they said, an “Internet Erase Button.”

Arguably, though, an “Internet Erase Button” or a “Right to Be Forgotten” might do as much harm as good. Forbes’s Adam Thierer rightly points out that press freedom and the freedom of speech are widely under threat. Sometimes the right to information ought to outweigh the right to privacy. What incentive will there ever be for a journalist to rake muck if the information can simply be taken down upon request? “Every blogger could conceivably be asked at any time to delete any comment on any post ever written,” Thierer notes. “Who makes these calls?”

Still, in two kinds of situations—personal information voluntarily submitted to websites, and information posted by or about children—the calls for an erase button seem reasonable. The scenarios posed by some critics of the plans (“Could a public figure claim ‘a right to be forgotten’ when a journalist pens an article about them beating their wife or committing corporate fraud?” asks Thierer) smack of straw men. Surely a better way can be found to manage the vast and confusing mass of data written by and about us online.

Maybe we don’t need to forgo the pen entirely in favor of the pencil—but in some cases, at least, we ought to be able to choose which tool we’re writing with.