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Categorization (labelling) is key for humans to understand the world around them. Our brains are not able to live in a world without categories. Try as you might, it ain't gonna happen. 
It's a functional device that we use, always have, always will. 
We use labels to manage our perceptions. It isn't possible for us to have 1 million labels to describe 1 million people, as it negates the point. 
The reason some people aren't happy with the exponential creation of labels for people is because it defeats the purpose of labels (to be able to generalise). 
The other argument against it is because everyone is an individual. EVERYONE. Whether they're young, old, tall, short, fat, thin, gay, straight, masculine, feminine etc. 
If you keep going with creating labels for every aspect of self then you'll eventually wind up at the individual level.
I mean, it's a pretty easy concept, right?
People hide behind labels to avoid responsibility. People use labels to gain benefits. People use labels to belittle and diminish value.
Labels can be used to come together, but of course they can be used to divide. It's "US" vs "THEM". >

People can use anything to avoid responsibility or gain things, the thing they're using to their advantage isnt the problem (ie. labels) but the tactic...which is called manipulation. So, I don't think that's a solid argument.
But I like that you mentioned the "us vs them" phenomenon. Labels can and do fuel that mindset, which isn't ...good. But I also think that the 'us vs them' has been a thing long before people started having "official" labels. People do the us vs them based on differences, its fueled by competition and to be better. So, point is, getting rid of labels won't directly get rid of this mindset either. 
Main point is that yes, labels can separate people and has done so even when you look back at history, but to a larger extent I'd argue they unite people.