In hinduism, Lord Shiva is depicted as half man and half woman to show this.
The Duality of Lord Shiva is the Unity within everyone of the Sacred Feminine and Masculine - an inherent and ever-present paired quality in everyone. it is to be found within, not from someone else. Shiva's "duality" is the perfect balance ALREADY in Shiva of the two - it is not dependent on another person putting it there. It is there already - but up to the individual, to develop, honour and manifest them for themselves.
A man is incomplete without a woman and vice versa.
As long as you think and believe this, you will never find true happiness, Joy, Inner Peace or Serenity. As long as you are dependent on the input from another person, to make you complete, you will never fulfil your own personal perfection - because nobody should ever be required to do that for you.
You - and only YOU - can make yourself complete. Input from somebody else, will always leave you INcomplete...