The Roman Catholic apostolate Courage, which assists those with a homosexual inclination to live authentically Catholic lives, embracing chastity, explains why it will not use the terms "gay" and "lesbian":
Q. Why doesn’t Courage use the terms “gay” and “lesbian”?
A. Courage discourages persons with same-sex attractions from labeling themselves “gay” and “lesbian” for the following reasons:
1) The secular world usually uses those terms to refer to someone who is either actively homosexual or intends to be. When a person decides to “come out” and say “I am gay” or “I am lesbian”, the person usually means “this is who I am – I was born this way and I intend to live this way. I have a right to find a same-sex partner with whom to have a romantic sexual relationship.” To “come out” as being “gay” or “lesbian” doesn’t usually mean “I have homosexual attractions and I have a deep commitment to living a chaste life”.
2) By labeling someone, we discourage those who may wish to try and move beyond homosexual attractions. Some people, especially young people, are able to further their psychosexual development with spiritual and psychological aid. If we labeled them “gay” and “lesbian”, they might think there’s no possibility of moving beyond these attractions.
3) There is more to a person than one’s sexual attractions. Even if one experienced same-sex attractions for most of one’s life, he or she is first and foremost a child of God created in His image. To refer to that person as “gay” or “lesbian” is a reductionist way of speaking about someone. We are even trying now to avoid using the term homosexual as a noun, or as an adjective directly describing the person (i.e. homosexual person). Although it takes more words, we prefer to speak of “persons with same-sex attractions”. Fr. Harvey has said that, if he could, he would rename his first book “The Homosexual Person” to something else like “The Person With Homosexual Attractions”.
There are people within the Catholic Church who might argue that those who label themselves “gay” or “lesbian” aren’t necessarily living unchastely. That’s true, but the implications of the terms in today’s society don’t commonly connote chaste living. Furthermore, they are limiting their own possibilities of growth by such self-labeling, and reducing their whole identity by defining themselves according to their sexual attractions. At Courage, we choose not to label people according to an inclination which, although psychologically understandable, is still objectively disordered.
See here: http://couragerc.net/FAQs.html
Courage refuses to use the words "gay" and "lesbian." Why then does Pope Francis use the word "gay"?