I completely agree. I have a 9 year old girl, a 5 year old boy and a 3 year old girl. Although I was working in fast food at 16, I didn't get a cellular phone until I was 24. Payphones or the house phone were the only way to communicate. It's very different than when we were growing up. I think that creates the fear: that a social norm in our generation can be fundamentally different in our children's generation. Our grandparents would say "wow, back in my day we had a party-line if we had a phone at all" and there's a lot truth to how upsetting seeing the world change completely in span of a decade can be, especially when you consider how that change impacts your understanding of your children. Our grandparent's generation saw change to the quality of life and removal of hardship: things they considered necessary to being a stronger person. How can someone become strong and independent if technology makes everything easier?
For our generation its basically the social relationships that are affected. We've removed the threat of crippling diseases, and most hunger. There are lot of benefits to having a constant connection to the outside world, but... there's a lot of downsides. Never really being alone, but also never really getting close to someone. Stretches of isolation or boredom are gone, replaced with constant insignificant communication via text message. You aren't ever really alone, so some people don't feel the need to communicate anymore than superficially. Being stuck with someone: waiting in line, working on a team, not being in a cubicle... things to which you can't bring a newspaper, but could easily bring a cell phone. That forced conversation, which often turns out pretty beneficial, is gone. Deep conversations are less frequent, the thoughtfulness required to write a meaningful letter, replaced by 140 character text messages. Conversation is abbreviated and less meaningful. I'm not sure that's a good thing for the kids to be doing, much like removal of all hardship wasn't necessarily a good thing for our previous generations.
This whole thing makes me think of a Star Trek NG episode, in which Q brings Piccard to his home. All of the Q's live forever and can control anything, so they've already experienced everything possible and have no challenges to overcome. They're sitting there in silence. That's basically what happens when you take away all hardship and preempt all communication with tweets. It gets really really boring. Nothing to overcome and nothing to talk about.