From a logical perspective that implication is true, choosing your sexuality implies you have a choice. However, I disagree with the premise that there is a choice to begin with.

I do not choose to be straight, I just am. I’m not gay, and no amount of choosing will change that. I’m a guy, and I can choose to look for a boyfriend, but it won’t change the fact that I’m attracted to women. Now maybe I discover that I’m actually attracted to both men and women, but I would argue that discovering is different from choosing. Choosing would mean that I can choose to not be attracted to a gender, which I can’t. I can only choose whether or not I act on it.