Answer:
Women don't have and don't want it. Men get it but sometimes they try to get rid of it. What is it?
A stylish winter top that covers your larynx.
They can be long or short; they can be grown or bought; they can be painted or left bare; they can be round or square.
Take one royal word in the plural and make it singular by adding one letter
They keep secrets locked away. And you pass through them each day. For each one there is a key, They respond to sesame.
It is something you will never see again.