It is the go-to source for breaking information - how is that not a news source?
News, as its meant in the lexicon, is factual based reporting. Twitter is the opposite. Its a hodgepodge of everything. You have to mine the data to find the gems.
Very few people (percentage of the pop) are on Twitter. People hear about Twitter via other media's amplification. So on its own, its a small platform with oversized influence.