What about just not caring whether you hurt someone's trivial feelings? That is becoming an important feeling in this ever-connected world.

Ugh, that should have said "important skill". Too late to edit now.

I wasn't getting much value out of Twitter anyway (not a judgement on Twitter's value, just on what I was getting out of it), and my business depends a lot on maintaining healthy relationships with lots of people, since we grow primarily by referral. It just made sense to drop Twitter altogether and tell people instead that I don't use it.

Sounds reasonable :-)