As far as I'm concerned, even the ridiculous acronym "LGBTQRSTUVWXYZ" itself is a farce. Why should any of those groups of people be forced to represent each other group in the first place?
Mainstream representations of sexual orientation are pretty f***ed up. If you are not heterosexual and especially if you choose to label yourself with any word in particular, you become a circus act rather than a human being and there is no turning back. (As an aside, there is no logical reasoning to the order of the letters nor any logic to grouping together sexual orientations and genders).
Also, the word "gay" as a signifier has very negative connotations. When one hears the word "gay", it signifies a particular lifestyle, not a simple sexual orientation of a human being, but rather once identified as gay, one is generally defined accordingly as: carefree, licentious, promiscuous, loud, colourful etc. We all know the stereotypes. If you are gay, you are expected to be an extroverted, hypersexualized, flamboyant comedy act and you essentially discard your humanity as you assume the label.
There is a major rift and distinction that I believe exists and needs to be made between the words "gay" and "homosexual". They clearly do not signify the same thing. Regardless of Morrissey's exact sexual preference, it is no wonder that he would prefer to avoid any labels, especially labels that signify clear misrepresentations to him as a person. I would do the same, and I do do the same.