Beyond the boundaries of anthropomorphic description lies the true essence of God the Father. The nature of anthropomorphisms has constantly been a struggle within theology. On one extreme there is the thought that since God's ways are not our ways (Isaiah 55:8-9) we cannot accurately describe him with human terminology, and on the other extreme is the thought that since all language about God is anthropomorphic then our theology is simply a mask for conducting anthropology.
Yes, the Bible teaches the incomprehensibility of God - God cannot be known unless he chooses to reveal himself. But (and I believe this comes from Barth), the mystery of understanding God does not come from the limits of language but from the metaphysical distinction between Creator and creation. In other words, it is not the fault of human reason and communication that keeps us from understanding God, it is the very essence of who he is in comparison to the very essence of who we are.
Abraham Heschel once wrote, "God's unconditional concern for justice is not an anthropomorphism. Rather, man's concern for justice is a theomorphism . . . Prophecy is essentially a proclamation that God's ways are not man's ways" (The Prophets, 2:51-52).
Thus, understanding the Almighty as Father pushes the limits of human reason, not because our language doesn't properly hold to the notion of 'abba' but because his ways are not our ways. Jesus also pointed to this when he compared the goodness of God the Father with human fathers (Matthew 7:9-11). All of the reasons why we do not understand or accept the blessings of fatherhood with our God is found in the distinction that our ways are different than his ways.
Of course, this does not negate the reality of his loving, fathering presence. The Bible is filled with accounts of God's enduring love for his people, a point which Jesus often reiterates with his own message. It is a covenantal love with his people, and it is an intimate love which whispers into the heart of everyone who hungers and thirsts for his presence. The prophetic message of Scripture is not a condemnation of our failure as it is a reality of our ways moving to destruction while his ways are moving toward life - a life to which he beckons us come.