he she or they?

So I am taking a Child Sexual Violence class this quarter.  Rather than being a social work class like I usually take, I decided to try to take a class in the Woman's Studies major.  It was very different than I am used to.  Our prof made us go around and say if we identify as a he/she/or they.  There were a few people in the class that said they identified with the sex opposite of what they were born.  I can understand that.  Gender identity, i get it.  But then our prof says she identifies as "they".  I was so confused.  I couldn't concentrate all class bc I was just wondering what that meant.  So thankfully to a woman I work with and Wikipedia, I found a definition of what it means.

The "singular" they is the use of this pronoun, where they is used as a gender-neutral singular rather than plural pronoun. The correctness of this usage is disputed.

So my next question is how can someone be gender neutral?  This is such a new concept for me!! So when you are born you do not identify as a gender? At all? Do you identify as a human? Or male AND female?? Looks like I need to be taking more Womans Studies classes!

The next thing that shocked me in this class was how casual everyone was.  People were dropping f bombs and talking about their personal sexual experiences.  Now I am not saying the Social Work program is Harvard by any means, but I guess taking this class has led me to really appreciate professionalism.   To say the least...

Gosh my life is so random! haha.