I have never considered the Holy Spirit in terms of gender, but the Father, Son, and ... Mother (HS) is an interesting perspective.

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The Catholic Church teaches that the Holy Spirit is genderless, but has always referred to the Holy Spirit as "He". This is because the Holy Spirit is of the same gender as the Lord Jesus. The Catechism of the Catholic Church teaches that we cannot properly assign a gender or genders to the divine, but when in our use of language, God must be assigned a gender, the Holy Spirit is referred to in masculine terms.