I'm not the only person who feels this way. C. Edwin Vaughn, longtime activist for the blind, also finds people first language offensive, for some of the same reasons I do: People-First Language: An Unholy Crusade.
The biggest problem I have with person first language is that it implies that autism (or whatever) is something shameful, awful or pitiable to be distanced from the person. The very act of separating the difference from the person only serves to highlight it and to say "hey, this person has this condition, but they're still a great person, it's just something they "have". Kind of like having a disease. Um, no thanks, that's not the way I want to be seen! Asperger's/autism is not something I "have". It didn't fall on my head from a tree one day and permanently stick to me. It is an integral part of me, of my being, thought and way of relating to the world around me. I am not ashamed of relating to the world differently, nor do I feel the need to distance myself from Asperger's.
Moreover, approaching Asperger's or autism in this way completely overlooks the positive aspects of being on the spectrum and that many of us on the spectrum would not choose to be "cured" even if that were possible. Yes, there are definite disadvantages to being on the spectrum, but it isn't all bad and there are advantages/bright spots that we enjoy which others do not. True disability advocacy does not pile shame on the disability.
Lastly, where does it end? Who gets to define what is a disability or a disadvantage and what is not? The suicide rate for LGBT teens is astronomical, as is violence perpetrated against LGBT people, particularly transgender folk....but we don't refer to anyone as "a person with gayness", or "a person with same sex attraction". We don't refer to non whites as "people of African (or whatever) heritage" or "persons with a higher rate of melanin". Being short is a definite disadvantage, yet I am not referred to as "a person with shortness" and little people are not referred to as "persons with dwarfism", at least they don't seem to refer to themselves that way. Why? Because to say those things implies that there is something so wrong about being gay, black, short, etc that it has to be verbally and mentally excised from the person, which, of course, also underscores the horror of the difference or disability. That isn't kind, thoughtful or helpful and I cannot endorse it.