What is Sexual Fluidity?

I recently read an article about the actress Cynthia Nixon saying that she chose to be a lesbian. (She was married to a man for many years when she left him for a woman.) By simply saying she "chose" to be attracted to the same sex throws a wrench in the progress gay activists have made. Choosing to be a sexual orientation gives those who are against gay rights, the evidence to say that being gay is a choice and it is not something someone is born with. Clearing up her statement, Nixon has said that she is bisexual and that it is easier for her to be with a woman than with a man. I think the part that has most people confused is the going back and forth. Nixon is considered to have sexual fluidity.
Sexual fluidity is when someone is attracted to the person not the gender. When looked at broadly, sexual fluidity is a beautiful concept because it means gender is not an issue. However, gender is a very big issue to the rest of our society. I also think this is more prevalent in women because society feels so uncomfortable with the idea of men going back and forth between sexes. Which is odd considering that in ancient Greece, it was considered an honor for men to have young male lovers. Today, it would be considered perverted and/or a trait of homosexuality.
And isn't sexual fluidity just another label for "bi-sexual"? What's the difference between the two? And why is it more acceptable for women to be sexually fluid than men? I don't believe that being bisexual is a choice, it is something you are born with. But I do believe that bisexuals do have the option of who they would like to be with.