Do you to choose whether you are Sunni or Shiite in Islam?

I am taking a world religion cl and on the first day of cl the professor was going around asking people what is their religious faith a girl said she was Muslim and the professor ask her if she was Sunni or ShiIte and she said neither and she just defensed her self by saying she believes in God and that is all that matter then the professor look at her and said ok like he was not convince or what she was saying was unheard of. In my opinion I agree with her as long as you believe in God and you are serving him it does not matter whether you are Sunni or Shiite, Baptist or Lutheran there should not be any split in any religion but of course there are a variety of people like religions out there not every one can be pleased