<My point was that I take offence at being accused of something which is untrue.>
"Person with same sex attraction" may be an accurate descriptor of one aspect of a gay person's life; but it reduces her or him to that one aspect.  It would be like describing you as a "person with avocado attraction", accurate but reductive. Of course, human sexuality goes to the core of the human person  --which is why you are not offended, or less offended, by pejoratives that don't pierce your self-understanding.
I'm really not sure why Cardinal Cupich's insight and suggestion about this is meeting any resistance. I sense that it has less to do with the suggestion itself and more to do with resistance to the cardinal personally (he seems to be a lightning rod in some quarters) as well as with the full, deliberate and willful intention to offend gay persons who have the temerity to claim the right to self-understanding and self-determination.