People who do not spend most of their time in front of a computer will call their friends directly, rather than checking Twitter.
Only the stereotypical geek sees an advantage in non-personal communication about personal matters.
That sentence is phrased for maximum humour, but with a kernel of deep insight:
a) If your mom was in the same room as you you would talk far more often with her than you do now. The easier you make something the more frequently it will happen. The more context y'all share about each other the more often y'all will talk to each other. And it's super hard to share context when you're far away from -- and out of sync with -- each other.
b) When you're face to face a lot of time you say things to each other where the only response is a grunt. That doesn't seem to be appropriate in IM or over the phone. The result: we're more careful what we say over the phone or IM. But if you can stop self-selecting what seems worth talking about you can find far more interesting conversation.
c) Just like not everything deserves a response, not everything deserves a response right now. If I know what is going on with my mother I'll have better conversation when I do talk to her. And it's better to lay the groundwork for it now, before we start talking.
d) We've had online communication for 10 years now, and it hasn't really cannibalized real-world interactions for the vast majority of us. What it has done is enriched and complemented them. In this case, twitter doesn't replace conversation, but it allows me to sidestep the tedious initial "how was your day, dear?" segways and head straight for the most juicy objects of conversation from somebody's timeline.
Conversation happens off twitter, but benefits from being rooted in it. This isn't purely synchronous IM or phone, nor is it purely asynchronous email. It's just a more organic way to manage conversation.