All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We are not aware of any evidence from the Book of Allaah or the Sunnah of the Prophet about this custom; rather, it is reported in the Sunnah that it is permissible for a woman to walk in front of her husband. For instance, the Prophet raced with ‘Aa’ishah in running at two different occasions and she won once.
However, the Sunnah clarified to us a high moral conduct for a woman as to how to walk in the street in general. The Prophet saw women walking alongside men in the street, so he ordered the women to keep away from the middle of the road and to walk on its sides. This is better for them because in this way they will not be mixing with men.
Allaah Knows best.