So many people like to think that the entire world can be sorted into neat little groups, with everyone given a label that fits them perfectly. But this never works. Everyone has different beliefs. Some will fit comfortably into the standard political spectrum, sure, but others don't. I've seen people who would mostly be labelled as liberal but also have other beliefs that are pretty firmly right wing. And labelling them as centre left is still misleading. And the worst part is that it means everyone gets lumped together. Surely you've seen Americans who hate anything resembling socialism because it reminds them of communism? And the reverse too anyone who identifies as right wing is automatically a Nazi. It gives people an excuse to be close minded too. Oh, you're a liberal, that means everything you say is invalid. Even if you disagree with someone's beliefs in general, doesn't mean that anything they say is automatically wrong. It happens with other groups outside of politics too. Any self proclaimed feminist who genuinely cares about equality is lumped in with the crazy sexist radicals. Defining people by their opinions is not only inaccurate, it's harmful to intelligent debate. I can pretty confidently say what part of the political spectrum I'd fall into, but going around using that particular label to define everything I do is not going to help anyone.
I think that sorting all political beliefs into two groups is harmful and stupid.