Why do Trinitarians call the Father, the Father?

Trinitarians believe that God exists as three distinct but equal persons (yes, I'm simplifying), known as the Father, Son, and Holy Spirit. They also believe that Mary was impregnated by the Holy Spirit: > Now the birth of Jesus Christ was on this wise: When as his mother Mary was espoused to Joseph, before they came together, she was found with child **of the Holy Ghost**. > — Matthew 1:18 (NKJV) > … that which is conceived in her is **of the Holy Ghost**. > — Matthew 1:20 How do Trinitarians explain why the title "Father" is given to a person in the Trinity other than "The Holy Spirit"? ### Note: What I am looking for is an official explanation by the Church that explicitly addresses this naming confusion. Ideally, there would also be an explanation of whether this event was effected by God's impersonal spirit (power), or by the third Person.