Perhaps I should not have used "right" or "left" for labels, but "good" and "bad". For instance, killing someone is bad. "Bad" is a label, but it easily conveys a meaning to the subject.
To go on, what about the terms "supply-side economics" or "Keynesian economics". Both are labels that quickly sum up two different economic schools of thought. Without the labels, I have to explain in detail what each means. With the label, I can quickly establish a starting point for a discussion.
So I don't understand your problem with labels.
Similarly, there are lots of people who call themselves "keynesian economists", but they range from total believers to people who admit that "supply-side economics" has a case too, through to folk who just admit keynesian economics has a point ot two going for it. Nor is this solely a matter of individual variation, because people argue over what the basic definitions are. What some people call "progressive", others call "socialist", and some no doubt call "reactionary". I admit, without the labels you would have to explain in detail what you meant, but I would argue that might not be too bad a thing. It might prevent a lot of misunderstanding, after all.
There's a further problem with labeling, and that is that certain labels become irretrievably linked to one another, but some kind of political osmosis. Thus, labels like "conservative" are linked to "NRA", "pro-life", "religious right", "republican", "capitalist" and "anti homosexual" (amongst many others). It has now got to the point that identifying yourself by one of those labels automatically (in the minds of others) gets you assigned to all of the others. But of course Conservative is a very broad term. Some are social conservatives, some are fiscal conservatives, to others political systems are what most needs to be addressed. Most would no doubt go along with many of the things on that list, but they wouldnt major on them. Few suited business investors are picketing abortion clinics. Some republicans ARE gay.
Does this matter? Well yes, because when labels are applied to people in that way, it denies their individualism and prevents them thinking through what they really believe, and that leads to trouble. Lumping people together into nice, neat little socio-economic groups is what leftists major on. This kind of thing stunts reasoned debate as well, which ultimately works to the detriment of the republic.