The New Testament scholar Murray Harris—who has been called one of the great Greek minds of our day—talks about why this is not true.
The following is an excerpt from his book Navigating Tough Texts: A Guide to Problem Passages in the New Testament:
It is true that in the Jewish Talmud and other Jewish documents we find statements such as “When a child experiences the taste of wheat (i.e., when it is weaned), it learns to say ’abbā and ’immā” (Berakot 40a in the Babylonian Talmud) (= our “dada” and “mama”).
However, even if the term abba began as a childish babbling sound (and this is far from clear), at the time of Jesus it was a regular adult word meaning “Father” or “my Father” (as terms of address) or “the Father” or “my Father” (as terms of reference).
That is, abba was not a childish term of the nursery comparable to “Daddy.” It was a polite and serious term, yet also colloquial and familiar, regularly used by adult sons and daughters when addressing their father. Ideas of simplicity, intimacy, security and affection attach to this household word of childlike trust and obedience. So to bring out the sense of warm and trusting intimacy that belongs to the word, we could appropriately paraphrase it as “dear father.”
If Paul had wanted to convey the sense of “Daddy,” he could have used a Greek word he undoubtedly would have known – papas or pappas that means “papa” or “daddy,” a child’s word for “father.”
There are four further reasons it is inappropriate to translate Abba by “Daddy.”
First, in all three NT passages where the word abba occurs (Mark 14:36; Rom 8:15; Gal 4:6), it is immediately translated by the term “Father” (the Greek articular nominative, ho patēr, used in a vocative sense).
Second, Jesus himself directed his followers to address God as “our Father,” pater hēmōn (Matt 6:9).
Third, each of the seventeen prayers of Jesus (not counting parallels) recorded in the Gospels begins with “Father,” presumably Abba in each case.
Fourth, for Christians, young or old, to address God as “Daddy” is totally inappropriate, for in English usage the term is too casual and flippant and unassuming to be used in addressing the Lord God Almighty, the Creator and Sustainer of all things, not to mention the fact that “daddy” is often abbreviated to “dad.”
It may be that an improper sense of familiarity with God on the part of some Christians prompted Peter to say, “If you address as ‘Father’ the One who judges each person’s work impartially, live in reverent fear of him during the time of your exile on earth” (1 Peter 1:17).
That is, to address God as “our Father in heaven” in the Lord’s Prayer is to remember he is the all-knowing and impartial Supreme Judge of every person, who therefore must approach him with reverential awe, not as though he were simply another commonplace “Daddy.”