You pose a very good question. YHWH is Spirit and "He" is neither male nor female. The thing is that Y'shua referred to the Spirit as "He" and we don't have any records (that I know of) where he used "She" for the Ruach.
John 16: 13 But when the Spirit of Truth comes, He will guide you in all truth. For He will not speak from Himself but He will speak everything that He hears. And future things He will make known to you. 14. And He will glorify me because He will take of my own and show it to you.
 Literally, he will not speak from "His own mind."
 The Spirit is not a substitute for YHWH, the Spirit of YHWH is the Father; however, the Father is ein sof (without end); therefore, our spirits are quickened by His Spirit to the degree that He reveals Himself to us. It is not possible that mortal bodies can contain the infinite presence; therefore, "He" speaks everything "He hears." In other words, everything from the Ruach haKodesh comes directly from YHWH.
The thing is, if you look back in history there were cult followings of a She component of YHWH that was joined with Asherah and so I think this is a slippery slope to start calling the Ruach haKodesh "She" because it divides YHWH into He and She elements and I believe this is a step right into paganism. Y'shua said there will be no male or female in the Olam Haba (World to Come); we will be spirit beings so it does not work to personify the Spirit as a She.
But that being said, it's understandable that the feminine movement is fed up with a male God and men who think they are gods because they are men. But there's got to be a better way to address this that bears equality that is based on the authority of the Word of YHWH, which is what was being addressed in Feminine Attributes appendix in the Aramaic English New Testament. But it's a difficult subject because if we go to Kabbalah, Zohar or Tanya then we get all sorts of pagan ideas and tales mixed in with truth. So, it seems that we are far better off to identify with YHWH's attributes within ourselves as per their Hebrew given gender as they are revealed because this is the nature of the Spirit of Mashiyach.
Another example along these lines is about the curse put upon a woman's "desire for her husband and he shall rule over you" - that curse must have unsettled an equality between male and female that existed before original sin. The curses upon man and woman are such that the curse upon man effects woman and vice-versa and none of this will be restored outside of Mashiyach.
So, rather than to call the Ruach a "She" we need to bump up our understanding to a higher level and look at our own destiny in Mashiyach which surpasses gender recognition, and also be very careful that we don't personify the Spirit of YHWH as something separate and different that YHWH Himself.
NOTE FROM THE REFINER'S FIRE:
While Hebrew the Hebrew language is extremely unique and different from most others, is important to keep in mind that languages, in general, are complicated, and often nouns rely on the word "the" (the definite article, adverb, preposition) to describe them.
For instance, in English, we use the word "the" as a definite article. However, in languages such as German and Spanish, all nouns are assigned a masculine, feminine, or neutral "gender" which can be seen in the word "the" which leaves a clue as to the "gender" of something (even though most things don't have a gender). Case in point:
In English we use "the" for everything - i.e., the spoon, the couch, the toilet, the boy, the girl, the dog.
In German and most other languages, a masculine, feminine or neutral article is used that assigns a "gender" to your subject, even though there is no rhyme or reasoning for it:
- The spoon: Der Löffel - Masculine.
- God: Der Gott - Masculine.
- Holy Spirit: Der Geist/Heiliger Geist - Masculine.
- The fork: Die Gabel - Feminine.
- The knife: Das Messer - Neutral.
- The ladder: Die Leiter - Femininne.
- The sofa/couch: Das Sofa - Neutral; but - Die Couch - Feminine.
- The toilet: Die Toilette - Feminine.
- The boy: Der Junge - Masculine.
- The girl: Das Mädchen - Neutral.
- The Dog: Der Hund - Masculine.
- The Cat: Die Katze - Feminine.
- The flower: Die Blume - Feminine.
- The car: Das Auto - Neutral.
- The balcony: Der Balkon - Masculine.
There is no rhyme or reason why inanimate objects are "masculine or feminine" - it's just how the language evolved.
Same with the various aspects of YHWH, the Holy Spirit, Yeshua, and the "genders" involved. Who today can truly know the rhyme or reason? YHWH is is not a gender and neither is the Ruach. Both are spirits. Yeshua is the only One who is actually a physical MASCULINE gender because He was a human male who actually walked this earth for 33 years.
Languages are complicated and one must never jump to conclusions about the meanings of certain words or concepts. They must always be viewed in context.