To start with, it should be mentioned that it is not always to take the witness of a woman as half of the witness of a man. In many cases, the witness of woman is equal to the witness of man, especially in matters related to the personal life of the woman herself.
Allah, The Most Merciful knows the abilities of His creatures. Women are delicate human beings because life needs them to be delicate to provide love and sympathy to her husband and children. Testimony is usually a challenge because it is countering another party who claims something different. In many cases, man is able to face this challenge alone but a woman needs another woman to share with her facing the challenge.
This is not the full reason but just to try to analyze the situation.
Allah The Glorious knows the full wisdom. All rules in Islam are based on The Absolute Knowledge, Wisdom and Mercy of Allah (SWT).