This is a tricky subject, and can't say I've ever quite got to the bottom of it. Since letting go of religion and the obsession of assuming the bible is the answer to everything, I've come to some interesting conclusions that work for me - so far!
The concept of God as our father is well grounded in scripture, particularly by Jesus. There's no disputing the image of a perfect father who loves us unconditionally, and will bring every person to the knowledge of their completion in him.
But there is also the concept of God as a lover woven through scripture as well. It's more subtle but is intrinsic to the concept of the "bride of Christ".
These days I don't quote verses to prove a point. I might dig around to get a feel for a subject, but Christ in me is my guide. So here's the thing that has gurgled around the back of my brain for some time. A perfect father is awesome, can't argue with that so I'm not dissing that aspect of God at all. But I am taking it a step further.
I think the idea of the Bride hints at a level of union and oneness with God that goes way beyond any Father/child relationship. Our personal romantic relationships go way deeper than parental ones. There is a softness, romance, mutual adoration and intimacy that supersedes all other relationships. We leave our parental relationships to unite with another person in way that is impossible with our parents.
Even though Jesus talked about his father, and there are things like the prodigal son, which are beautiful metaphors, he hinted at something deeper many times as well - the father and I are one etc.
Paul and John talked a lot more about an intimacy that you would never describe as fatherly. In fact, father implies separation - sure, a loving father who is besotted with his children, but never the less, separate.
Now that we are one with God in every sense, that father/mother model has been outgrown. We are now old enough, as it were, to be lovers. To enter a whole new realm of love. A unity and oneness with all he is and all he has created (and expressed toward each other) that surpasses the need for the type self deprecation we associate with an authority figure (no matter how benign they may be).
The implications of this have been creeping up on me and creating a whole new sense of who God is and how I was created to relate to him. We are equals!! Of course, he is completely "omni" everything and I'm not like him in that sense, but he wants me as an equal, like a lover, no secrets, everything shared, neither lording it over the other. Just a beautiful oneness built on God's initiated passion that has drawn me into his arms.
Dare I also suggest that this surpasses all concepts of gender, God being completely female and completely male, thus completing us on every level no matter what our gender/sexuality is (although this is another huge topic!).
Perhaps the whole concept of lover is really what Jesus meant by "sending the Holy Spirit to live in us". There is a huge realm opening up for me that transcends culture/religion/scripture/tradition and all the bondage those things create, and frees me to to embrace Holy Spirit.
I've always thought that addressing God as Father just never really expressed it right. I'd try Jesus or Spirit or Lord or whatever, but nothing does the job. I'm tempted to call him Lover! No more "Father God I beseech you to pour out your blessings, blah, blah". Now its just "Hey Lover, what are you doing, can I help, or do you just want to hang out, maybe we could make love!!"