It is difficult therefore to escape the conclusion that Jesus said ‘Abba’ to God for precisely the same reason that (most of) his contemporaries refrained from its use in prayer – viz., because it expressed his attitude to God as Father, his experience of God as one of unusual intimacy.
― James D.G. Dunn, Jesus and the Spirit: A Study of the Religious and Charismatic Experience of Jesus and the First Christians as Reflected in the New Testament