school got involved with a twitter account?

[Rachel Mcgonez]

So some person at my school (whom I don't know) created a Twitter account which essentially makes fun of a teacher. Many people followed this account, including me. However, I was unknowingly following it because at the time I also had requests for a few other followers so I didn't pay close attention to who I was following. I guess my story doesn't really matter here. Anyways, today, all the people who were following the account and I were called down and we were informed that the administration knew about the page and had contacted the police. They informed us that we must unfollow the page and that they emailed our parents. They also looked at each of our own pages, for not specific reason. They said that whoever created the page was committing identity theft, which is understandable. However, I do not see why me and the other followers got in trouble and I really don't see why they had to inform our parents. I can see giving us a warning and maybe taking us to a computer and having them (the administration) watch me unfollow the account. But emailing my parents?
Is that legal, or right? Can they actually do that? For some reason I feel like they can't. Also, some of the people's parents they emailed are 18 so isn't that also technically wrong?
I would really prefer a perspective of someone who is actively involved in the law, and I also am not looking for a lecture on social media and what not.

[boop]

You (probably) got in trouble because you were following it, which they would see as supporting the group. Plus you didn't report it, so you were basically involved, in their eyes.

They informed your parents because it's a nasty form of bullying. Teachers can be bullied to suicide too.
So, for example, if you were bullying someone inside school, they would call your parents because what you're doing is against the law(in most places).

So, yes, they're entitled to email your parents.
However, since some students are 18, I'm not sure why they would contact their parents. That could be considered wrong but if the student is living under their roof still, that's enough of a reason for them to contact the parents.