Why do asexual people need to label themselves?
While it may seem silly that there are so many 'made up' words surrounding things like asexuality, their usefulness cannot be understated. Words exist so that people have the language to talk constructively about issues that are important to them – and sexuality does have a significant impact on many people's lives. These days it is easy to find testimony online that people can feel much less lonely when they find a term and community to help them understand what they were feeling.
Terms like orientation labels also create the conditions for greater awareness, and contrary to what it might seem, they do not need to be used to divide people into separate camps. Sadly, it's always possible to use words in a harmful way, and these terms may play a role in enabling othering behaviour to occur more easily. However, in such a case, it is always the perpetrator at fault rather than the words themselves.
More generally, symbols (such as words) demonstrate unity, pride, shared values, and allegiance to one another, as well as communicate ideas, concepts, and identity both within the asexual community and to mainstream culture. Giving people something to associate themselves with provides normality to what is an overall socially-isolating situation.