This is the assertion of Kevin Giles in The Trinity and Subordinationism (IVP, 2002):
Here it is to be recalled that in the Bible and in the early church, the title “Father” is used in two cognate ways: in reference to the Godhead and to the person of the Father. Torrance argues that the Cappadocians’ error was to completely conflate these two meanings of the title “Father.” In the former sense, the Father (i.e., the Godhead) may be thought of as the source or font of all being. In the second sense, the Father (i.e., the Father of the Son) is he who is coequal and coeternal with the person of the Son and the person of the Holy Spirit (43).
In support for his claim that the Bible and the early church use Father to refer to the entire Trinity, he points to Torrance, The Christian Doctrine of God, 137, 181; Trinitarian Faith, 241; and LaCugna, God for Us, 71.