This points to community. God is a community in Himself - Father, Son and Holy Spirit. We are made in His image, so we also need to be in community with one another.
It also implies communal worship and prayer where we are in agreement, and everyone is of equal status before Him. Therefore every person's unique relationship and experience with God is equally valuable.
The moment a baby is born into a family, it is to be expected that the parents will care for, feed and protect the baby. So we can also be assured that our Father will care for, feed and protect us.
There is no need to earn His love by proving ourselves worthy. He already loves us and always will just because we are His children.
As a Father, God not only loves and forgives us, but He also teaches and disciplines us. So He is the God of both the OT and the NT.
God is not distant but is always near to us. Just like how a child can run to an earthly father who lives in the same home whenever there's a need, we can call out to Him anytime.
For many believers, our perception of God the Father have been marred by the imperfect parenting we have received (or possibly also from the influence of imperfect spiritual elders/parents we have encountered). We need to examine ourselves and repent if we have been a stumbling block to anyone. We also need to seek God’s healing and restoration if anyone has caused us to stumble.
3. Our Father
We are all His children and belong to the same family. He has no grandchildren and every believer has direct access to Him as His child. There's no need to go through one's earthly parents or anyone else.