A type of speech intended to separate the disability from the person. It has become well accepted by non-disabled people who try to advocate for the disabled, but beyond that has numerous flaws. Disabled and particularly autistic people have complained that it treats the disability like something too terrible to be mentioned, something unimportant, or something that can be easily separated from the person. The awkward phrasing also has the tendency to bring out the disability.
In some cases, this form is grammatically correct, if the name of the disability cannot be transformed into an adjective. An often used example is "child with Down's Syndrome" instead of "Down's Syndrome child". No attempt can change Down's Syndrome, cerebral palsy, muscular dystrophy, etc. into an adjective.
I am autistic, not a person with autism. I could use people first language by calling myself a person with femaleness. Everyone would think it odd, but my gender is less essential to who I am than my neurological configuration.