Before you criticize the argument, "People are born gay", you need to have an understanding of what the argument actually entails. When you hear others claim "homosexuals are born gay", they're referring to the fact that sexual attraction is affected by our DNA. Sexual attraction may not be present in our earlier years, but whether we'll be attracted to the opposite sex or not will be programmed in us (our attraction to other people will become less dormant as we grow older).
It's sort of like puberty. At which point in our lives puberty effects us is programmed in our DNA, but it lays dormant until later years. This is more along the lines of what people mean when they say, "People are born gay".
You are right about one thing though, whether we act on sexual impulses or not is a choice.
This is where we must be careful with our wording. Sexual activity is a choice, but sexual attraction is not.