It isn’t quite right to say that the Aramaic “abba” means “daddy.” In other words, to call the God of Abraham, Isaac, and Jacob “daddy” at the outset of our prayers is a bit too casual and irreverent. Philip Ryken explains.
“To call God ‘Abba, Father’ is to speak to him with reverence as well as confidence. Abba does not mean ‘Daddy.’ To prove this point, the Oxford linguist James Barr wrote an article for the Journal of Theological Studies called ‘Abba isn’t “Daddy”.’ What Barr discovered was that abba was not merely a word used by young children. It was also the word that Jewish children used for their parents after they were fully grown. Abba was a mature, yet affectionate way for adults to speak to their fathers.”
“The New Testament is careful not to be too casual in the way it addresses God. The Aramaic word abba appears three times in the New Testament (Mark 14:36; Rom. 8:15; Gal. 4:6). In each case it is followed immediately by the Greek word pater. Pater is not the Greek word for ‘Daddy.’ The Greek language has a word for ‘Daddy’ – the word pappas – but that is not the word the New Testament uses to translate abba. Instead, in order to make sure that our intimacy with God does not become an excuse for immaturity, it says, ‘abba, pater.”
“The best way to translate abba is “Dear Father,” or even “Dearest Father.” That phrase captures both the warm confidence and the deep reverence that we have for our Father in heaven. It expresses our intimacy with God, while preserving his dignity. When we pray, therefore, we are to say, ‘Our dear Father in heaven.’”