Unless you are working as a journalist, or for some other reason you need to respond immediately to world events, you could just abstain.
True for the most part. But occasionally there's good reason to want to know some information sooner rather than later: outbreaks of war, dangerous/breaking events in your localised area, dangerous weather alerts etc.
So to avoid twitter, you can subscribe to the primary source.
At least it used to be this way. But then a few official places that annouce things have turned to use twitter as their primary source.
If CNN has decided not to cover the protest happening outside your downtown office and you don't want to go up to a rowdy crowd to figure out what's going on, Twitter would (have) be(en) the place to drum up intel (with which to decide if you need to go home early that day or not).