The problem i find, if there is one is as follows.
Asexual folk want to be called asexual, and they are using this in regards to their sexual orientation. Now, if there wasn't a perfectly useful word already in existence, then taking another word that does not mean what you think it means and using it in an "off label" manner, would be fine. There is no word to describe it so you have to make due.
Problem is there is already a word out there, celibate. There is no reason to not
use a word that already has a meaning, and certainly no reason to cause a fuss if someone doesn't want to call you said word.
It makes no more sense to call someone who does not want to have sex asexual, than it is to call someone who likes to chase string, eat fish, and sleep 18 hours a day feline. Being similar to something does not make you that thing, no matter how much you want it to.
For purposes of social getting along, sure i'll call someone an asexual, doesn't take any additional effort on my part. But if we are debating the use of the word, it is simply silly to say someone is asexual. Human beings are not asexual, plain and simple.
There is no real problem, simply that it is silly. I would have the same reaction if vegetarians wanted to call themselves herbivores. No they are not herbivores, they are omnivores that for any number of reasons don't eat meat.
Lets take it away from the realm of humans for a moment to outline why it induces an eye roll in some forum members. ( As an aside, this anecdote is based largely off of a real life incident involving an employee at my old job.)
I bring knives into work, not a job that needs knives, just an average office job. I clean them, sharpen them, etc. Now when i get told i cannot bring weaponry into work i then tell the boss, "But they arn't knives, they are collectables. ".
And there you see the problem, while i think of them as collectables they are knives, and prone to any knife related issues. Sure i can request you refer to them as collectables, but that doesn't change the fact that they are knives, and doesn't make the person calling them such some kind of ******* if they chose not to want to call them by a less descriptive name.
Where does it end? Does one get to say they are a plant because they really like the sun? Does one get to claim to be their favorite animal if they display enough traits of it? And for that matter who gets to decide when someone can claim a falsehood, and not be called on it? Is there some kind of scale?
I actually knew a gent that wanted to be referred to as a squirrel, seriously. He would get just as offended if someone refereed to him as a person as an asexual would if referred to as celibate. But how many people here would make the case that if we just ignore the definition of squirrel , he would fit within it?