I would like to address this to ... your students:
It is okay if you don't see the value in twitter. It takes time to develop relationships from your network and to feel comfortable enough to share with them and have them share with you.
Obviously, many people feel twitter has value for their personal and professional lives. That doesn't mean that twitter will work that way for you.
I would suggest you give twitter some time and attention. Broaden who you follow and read what they write. Don't feel bad if you only "lurk" because everyone on twitter lurks sometimes. Then, if you still don't see the usefulness for it then don't use it. No tool is right for everyone.
If twitter doesn't work for you, I would encourage you to find other avenues to develop a network. The worst thing you can do is isolate yourself from the collective intelligence (and sometimes wisdom) of the rest of us.