My mom says that facebook stalks people. Is this true? If so, how is it dangerous?

Not in the means most people mean, when they say "stalker".

However, it does gather as much information as it can about your lifestyle, for purposes of advertising.  Most people don't realize how much information they allow Facebook (and other internet media) to gather about them.  >  Of course, if your mom uses a credit/debit card to shop with .. They're also gathering information from that.

No, not in the sense of which your mum put it (people aren't stalking you)

However.. Like many other sites. Facebook collects information about you.. To target advertisements towards you. (you can stop this tracking by using an extension called Disconnect and disable the 3rd party cookies in your web browser in the settings somewhere)

Facebook itself doesn't stalk you, though it may use information you provide in ways you wouldn't want. It may also sell on your information to other web users.

The real danger, and this is probably what your mother is worried about, is that scammers and paedophiles infest social media sites like Facebook and they are most definitely dangerous. Be very careful about trusting people, no matter how "nice" they seem to be. On the Internet you can say anything you liked about yourself and it need not be true at all.

Well my dad has facebook and on his list of suggests of people to add it has people from his work and people from my school. He has not put any information into facebook about where he works and I have no idea why its suggesting people that I go to school with, so I think facebook is very dangerous. There's no privacy and there are all sorts of crazy people on there. Join if you want, but I can certainly see your mum's point...