What's the big deal with identity?

On many of the threads about homosexuality, it is common to find remarks like the following:

Instead of “gay man” or “lesbian woman,” I prefer to use the term “person with same-sex attraction or SSA,” since the other two go well beyond a neutral description of the person’s predominant attractions by implying that the person identifies with his or her temptation.

Personally, I must admit I have a hard time understanding the thought that statements like these are trying to express, so I was hoping that others on these forums can help me out by answering the questions below.
[LIST=1]
*]What is an identity?
*]What should be included in an identity, and what should be excluded?
*]Are the ingredients of one’s identity always chosen?
*]The classical sources of moral theology do not discuss identity. What are some Catholic resources for understanding identity and how it relates to morality?
[/LIST]

Let me add that my interest in this issue is abstract, so even though I motivated the problem with the example of homosexuality, nobody should feel like this thread is really about that or that we have to stick to that topic.

Identity isn’t an issue.

At issue, is whether or not a person with same sex attraction is determined to accept the homosexual lifestyle and become noncelibate.

I have been asking that question in both gay and ex-gay circles for years and nobody has ever given me a coherent answer. The gays say gay is their identity but can’t say ***what ***an identity is and can’t give me an example of an identity other than gay. The ex-gays say gay is not an identity, our identity is Child of God, but can’t say what an identity is or give me another example either.

Personally I think an identity is whatever makes you you, something you do not share with anyone else, and if two people have the same identity then they are one and the same person. So if gay is an identity, all gay people are really one and the same person. Which is absurd. Therefore gay is not an identity.

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