I know that Twitter is US site but I still find it strange when people talk about balanced political views and talk only about 2-sides. Yes it is one more than in China but still...
I'm not from the US, but from India, and it's the same here. "Left" and "Right" may be misnomers, but there are effectively two main blocks at the national level, and supporters of each block get slotted into one of the two. Of course there are disagreements between members within each of the two blocks, but ultimately all the fine distinctions boil down to which of these two a voter would choose!