This weekend at Church, a speaker said that “Abba” means “daddy.” Notwithstanding the popularity of this idea, it is simply false. As J. Ashton wrote in the Anchor Yale Bible Dictionary on Abba:
[T]he form has been explained as a rare vocative (in which case it could just as well be Hebrew as Aramaic) or as derived from children’s baby talk (cf. “Papa,” “Daddy”). If the last explanation were right, then the use of abba as an address to God in Mark 14:36 might be thought to imply a special, indeed a unique, intimacy. This view was held at one time by J. Jeremias, but he later came to regard it as “a piece of inadmissible naivety” (1967: 63). Wrong as it is, it deserves mention not only because of its extensive dissemination beyond the walls of academia but also because its influence can be detected even in the work of respected scholars such as J. G. D. Dunn (1975: 21–26; 1980: 22–23) and is explicit in the most recent writing of M. J. Borg (1987: 45). Apart from the intrinsic unlikelihood of the idea that Jesus ever addressed God as “Daddy,” the suggestion is ruled out of court by one important fact: wherever abba is found with the meaning “father” or “my father” (in Mishnaic Hebrew or Targumic Aramaic), it is equally employed of the fathers of grown-up sons. One instance cited by G. Vermes (1983: 42) is Judah’s threat to his unrecognized brother, Joseph, in the Tg. Neof. version of Gen 44:18: “I swear by the life of the head of abba, as you swear by the life of the head of Pharaoh your master …” And as J. Barr (1988) emphasizes, inferences concerning the meaning of words must be based upon function, not upon origin or derivation.
Ashton, J. (1992). Abba. In D. N. Freedman (Ed.), The Anchor Yale Bible Dictionary (Vol. 1, p. 7). New York: Doubleday.