For the person with the disability or their loved ones, it makes it better, because you are seeing them as a person first. When I had cancer and was going through chemo, no one ever introduced me as a cancerous man. I was a man with cancer. I am a person that has cancer. I am not cancer that has a person. The same goes for people with other disabilities. People that have disabilities or illness do not want them broadcast for everyone to hear, especially if its mentioned before what they really are. It's putting a stigma out there that is negative and everyone is so much more than their disabilities.
For example, someone with a cognitive disability (formerly called mental retardation) should never be referred to as a retarded person, retard, or a 'tard. If you must refer to their disability (which should be rare), then it would be that person with a cognitive disability. I have found that in most social situation, mentioning the disability is unnecessary because most people will figure it out for themselves.
I have never mentioned this before, but I have fathered three children. I had a son that would be 18 this year. He was born with a cognitive disability and was labeled mentally retarded. He lived until he was 9 years old and died from a long battle with a very rare brain cancer called Glioma. During his 9 years, he had to endure classmates calling him a retard. While he tested very low on IQ and other tests that measure cognitive development, he was smart enough to understand that other classmates were being mean to him based on his disability. He said to me one day, "I wish I smart so my classes would like me, but I can't help it." Nothing has hurt me worse as a parent than seeing my kid being discriminated against for his own disadvantages. Thankfully, he is in a better place now where that is no longer happening to him.