In Orthodox Christianity, God the Father is a Spirit, God the Father is also Holy, therefore, God the Father is a Holy Spirit, right? If God the Father is not Holy and a Spirit, a Holy Spirit, then what kind of Spirit is He, surely it makes logical sense to call God the Father a Holy Spirit, right?
In Orthodox Christianity, the understanding of the nature of God is rooted in the doctrine of the Trinity, which consists of God the Father, God the Son (Jesus Christ), and God the Holy Spirit. Each Person of the Trinity is fully and completely God, yet they are distinct from one another.
When we refer to God the Father as a Spirit, we are acknowledging His transcendent and immaterial nature. However, the term "Holy Spirit" is specifically used to refer to the third Person of the Trinity, who is distinct from the Father and the Son. While it is true that God the Father is holy and is Spirit, Orthodox theology maintains that the title "Holy Spirit" is reserved for the specific Person of the Trinity who is known as the Holy Spirit.
Thus, while it may seem logical to call God the Father a "Holy Spirit" based on His attributes, Orthodox Christianity emphasizes the distinct roles and identities within the Trinity. The Father is not referred to as the Holy Spirit because that title is specifically associated with the third Person of the Trinity, who has a unique role in the economy of salvation and in the life of the Church.
In summary, while God the Father is indeed holy and a Spirit, He is not called the Holy Spirit because that term is reserved for the distinct Person of the Holy Spirit within the Trinity.