I think the unspoken reason why a lot of christians would prefer gay people to say "I have same sex attraction" rather than "I'm gay" is that saying "I'm gay" tends to imply gayness as a stable feature of someone's personality --

Whereas "I have same sex attraction" tends to quietly imply an addendum: "...until I am healed of it"

But many Christians don't want to say this outright, which is why they instead argue, "saying 'I am [x]' is the same as reducing oneself to [x]'"

This argument is easily identifiable as nonsense for any other adjective besides "gay"

I'd honestly rather people consider homosexuality an unhealable disability than consider it something that one can mature out of

(I'm not saying I do consider homosexuality to be a disability, but I'm also not saying what I do consider it to be, because I don't know)