Is it appropriate to ask your old elementary school teacher to add you on Facebook?

[Aurek]

Teachers love finding out where "their kids" are and how they're doing. Facebook is awesome for that. But they also like having their privacy, and reserving their social media pages for their peers, families, and associates. For that matter, I like my teachers to have some privacy too. Do you really want to find out your second-grade idol is now a picture-posting midwife or bar-hopping with college guys or something? O.o

You did nothing wrong; a Facebook private message is the equivalent of an email, and they're treating it as such. It's your call as to whether you withdraw your friend request or not; just be aware they probably won't add you, and it's absolutely nothing personal.