Bluntly, because when we still had such things as sodomy laws and the "gay panic" defence[0], society wasn't ready to deal with that nuance in a productive way. You need to keep your message simple when you're trying to change deep-seated beliefs, lest people perceive a loophole in the minutae to excuse clinging to their prejudices.
Both the notions "anything but complete heterosexuality is unnatural" and "sexuality is a strict binary" were widely-held misconceptions in need of correcting, sure, but it was prudent to dismantle western sociey's attachment to the former before tackling the latter. If the idea of sexuality as a gradient had been popularized first, it would have been misused as a stick to beat down the campaign for acceptance of minority sexualities: "Why should we allow homosexual behaviour? As you've just been telling us, it's not a binary thing, so surely you're all a little bit straight? Sorry, you'll just have to put up with living according to only that part of your inner self. Stop complaining - according to you, we're all a little bit gay, and you don't see us grumbling about not getting to act on it."
Maybe look at the various social consequences in places where the "immutability" line is or has been sold, versus places and times where it isn't or wasn't.
there's a spectrum of sexuality which expresses itself in different ways to different degrees in different people /= sexuality is [almost] invariably mutable
Especially when the argument over mutability is usually framed as "people attracted to the same sex or inclined to gender nonconform are bad influences on others and they can and must adapt their behaviour to conform to social norms" vs the argument that it's imposing the obligation to change one's sexuality that causes some people psychological harm
Both the notions "anything but complete heterosexuality is unnatural" and "sexuality is a strict binary" were widely-held misconceptions in need of correcting, sure, but it was prudent to dismantle western sociey's attachment to the former before tackling the latter. If the idea of sexuality as a gradient had been popularized first, it would have been misused as a stick to beat down the campaign for acceptance of minority sexualities: "Why should we allow homosexual behaviour? As you've just been telling us, it's not a binary thing, so surely you're all a little bit straight? Sorry, you'll just have to put up with living according to only that part of your inner self. Stop complaining - according to you, we're all a little bit gay, and you don't see us grumbling about not getting to act on it."
[0] https://en.m.wikipedia.org/wiki/Gay_panic_defense