Precisely. Choice or no choice (or "nature vs nurture") has nothing to do with LGBT rights. Trying to defend who you are by saying "I was born this way" is just handing a stick to those who want to beat you.
If a religious sect believes that you are sinful, telling them "I was born this way" isn't going to cause them to say "Oh? Well then, you're not sinning after all."
If people have a compulsion to abuse folks like you, telling them "I was born this way" isn't going to cause them to say "Gosh, I'm sorry. I take it all back."
If people at the courthouse don't let you take certain legal acts because it doesn't seem appropriate to them, given "how you are", telling them "I was born this way" isn't going to cause them to say "In that case, certainly we can help you."
Every advancement made over such obstacles has been achieved in a court of law, and courts of law only care about balancing freedom versus equality. How the litigants were born never influences their decisions. It's irrelevant, and it sidetracks a debate that SHOULD be strictly about freedom versus equality.