Many people will resist using the word disability to describe dyslexia. Yes, the term learning disability is not particularly attractive. The real issue is the use of the word learning. We dyslexics do have a disability, but it is related to reading text, not to learning.
Some people don’t like the word, believing that it implies that something is broken or seriously amiss, and will choose the word "difference" instead. Others will use a different euphemism, such as "special" or "uniquely skilled." We often avoid using the word "disability" when first explaining dyslexia just to avoid triggering this negative association.
However, it is important to remember that never saying the word is similar to renaming an up-and-coming neighborhood in order to sell more homes: suddenly the sketchy south side of town is called SOMA for “South of Main” in an attempt to distance it from it's former reputation as a tough neighborhood to inhabit. It's still the same neighborhood, though, and if you live there, you are less interested in what it is called than in how you will be treated.
The key here is to get over any stigma you feel about the word disability itself. We all have weaknesses, and you should be comfortable discussing them. Being able to say that you are a person who has weaknesses shows humility. Similarly, saying that you are a person with a disability should not convey that you are incapable, but merely that there’s a specific life area where you’re not part of the mainstream.
In a legal context it’s critical to understand that dyslexia and specific learning disabilities are categorically included under the term disability. It is important to maintain this designation when communicating with a school or an employer because of the legal rights and protections that come with the term. Separately, understand that the word disability is one that generations of people have fought to create. The Americans with Disabilities Act
is not called the Americans with Differences Act. Under that law, the process of "learning" (and with recent amendments, "reading," specifically) is part of the definition of “major life activities” that can be affected by a disability. Dunking a basketball would not be considered a major life activity, so the inability to dunk is not a disability. But if you have difficulty doing something that everyone expects mainstream people to be able to do, you have a disability.