Abba suggests an image of unceremonious closeness and warmth, of undaunted familiarity and at-homeness with God.
What are we to make of the fact that Jesus addresses God not only as Father, but as Abba, Daddy? According to Joachim Jeremias, this venture in language ‘was something new and unheard of’, perhaps revolutionary. This is a matter of scholarly debate. What is not debatable is the striking fact that that more than sixty times in the Gospels, nearly forty times in John, Jesus uses the phrase ‘my Father’, which has no parallel in the Hebrew Bible. And according to Jeremias, no parallel in all the literature of Judaism. No biblical Jew would have dared conceive of such a standing with God. It would have been blasphemously familiar, which is the very accusation the Jewish leadership leveled at Jesus.
The plain and astonishing fact is that this language was commonplace for Jesus… [Author gives many examples]… Again and again Jesus refers to God not only as ‘Father’, but as ‘my Father’. He refers to himself not only as ‘a’ son but as ‘the Son’. In terms of the Bible, Jesus’ relationship with God, whom he called ‘Father’, ‘my Father’ and ‘Abba’, is in a class by itself…
The relationship between Jesus the Son and the God he called ‘my Father’ was an exclusive and intimate relationship so unthinkable to the Jews that they took up stones to kill him for blasphemy. For in ‘calling God His own Father,’ he was ‘making Himself equal with God.’ (John 5:18). They could only take his familiarity as undiluted arrogance.
The Shack Revisited, C. Baxter Kruger