(1) Heterosexuality and homosexuality will not be viewed as equal as long as this argument is made by straight 'supporters'. No matter how anyone tries to sugarcoat it, this argument actually reads: "Well, heterosexuality is the default, preferable, 'natural' norm. But, if some people *really* can't help if they were 'born' outside of it - if they cannot attain this norm - then, perhaps it is acceptable if they are homosexual." If you don't believe this is true, try asking most of the people who say this how they would feel if it turned out that homosexuals were choosing their sexual orientation. You might have to push a little bit. Many people will initially fight the hypothetical. But many of them will eventually admit that they wouldn't be as ok with it. I've even heard some people say that this would "threaten their sexuality."
(2) There is ALWAYS a choice. Always. If you are queer in any sense, and you acknowledge this, even if it's only to yourself - then you have made the choice to do this. If you have a queer partner, if you go out to queer events, if you are active in your community, then you have chosen to do these things. You were not born doing them, it turns out. Presumably you have made these choices because they are good, positive options for you, or at least, better and more positive than the other options you see for yourself. There is nothing whatsoever wrong with making these choices. They should be celebrated and encouraged, just as people's heterosexual choices - to speak of their opposite-sex partners, to keep pictures of them at work, to be openly affectionate in public, to get married, to talk about having kids with their partner, etc - are already celebrated and encouraged. Society already, by and large, restrict queer people's ability to celebrate these choices - and talking about them as though they are not choices - as though they are something unpleasant that cannot be helped, kind of like an undesirable sore that won't heal no matter what you try - only makes it worse.
(3) It brings out the most bizarre phobias in people. This past year, I had a straight friend say to me, "Well, I'm ok with homosexuality, because that's not a choice. But I'm not ok with those trans people. I think that's a choice. They were born one way, just like homosexuals were born homosexual. They should live according to their birth sex." I was too dumbfounded by this incredibly perverse argument even to respond. I just stared at her.
(4) It confuses the issue for bisexuals and pansexuals. I have heard people argue that bisexuals and pansexuals could choose to be with opposite-sex partners, so it was wrong of them to be with same-sex partners (again - the argument that heterosexuality is preferable, and it's only ok for those who *cannot* have opposite-sex partners to whom they are attracted to have same-sex partners). So, the "it's not a choice" argument does not even awlays refer to whether you actually choose your own sexual orientation; in some cases, it just refers to whether you could be with an opposite-sex partner.
(5) So what if it was a choice? Hypothetically, what if someone right here, right now, said "I want to be gay" - and was able to effect a change in their sexual orientation? Would that make them bad? Sinful? Evil? Wrong? I have no opinion on whether some people can or cannot do this - some people believe that they have (Queer by Choice), and I certainly have no evidence to rebut or support their claim, but I have come to believe that it should be irrelevant. The Religious Wrong would say that all queers are making "lifestyle choices." I now believe that the response should not be, "It's not a choice!" but "So what if queers are?" I know that most people believe that they did not choose to be queer. But ask yourself - what part of your identity would be wrong even if it was a choice? If you could have chosen it, rather than discovering or realizing it, then why would it be anything worse?
(6) I can't speak for any other country, since I've only ever been an American, but a large part of my American identity is the freedom to live not only as I was born, but as I choose. This is no new, radical, progressive, or revolutionary idea cooked up in 21st century San Francisco or Seattle. For example, this country has long embraced freedom of religion - something that one can be born with (e.g. some Jews believe that their Jewishness is so innate that it is independent of any conscious choice they make once they are old enough to understand Judaism doctrinally) or that one can choose (e.g. converts to all religions) - and we don't give a damn whether it's one or the other. For many years, I was interested in converting to Judaism, and I was open with virtually everyone I knew about my interest in converting. Although I heard every opinion under the sun, from supportive to egregiously anti-Semitic, no one EVER told me that my secular rights and freedoms should be less than those of other Jews if I converted, because I would be making the choice to convert, whereas the latter group was born with it. A deeply held religious identity was viewed as something worth protecting; whether it was bestowed at birth or acquired later was irrelevant. And so too should sexuality be - innate (and potentially chosen?) sexual orientation, and also lifestyle choices made on the basis of sexual orientation.
EDIT I know there are some controversial ideas in this post, and if you disagree with anything, please feel free to discuss.