It infuriated the religious Jews of Jesus' day who considered it blasphemy to call God their father, because they understood that to mean they were equal with God (John 5:17-18).
This title has become so common in the church today that we, many times, don't perceive its real significance. The revelation that we are instructed to call God "our Father" reveals the kind, gentle, loving nature of our God (1 John 4:8). Paul used the term "Abba Father" (Romans 8:15), which is an affectionate term that a young child would use for his father, corresponding to our English word, "daddy."
We are being instructed here to recognize our relationship with God and praise Him for it. It's a relationship that goes beyond any human relationship we could ever have here on this earth. It's a relationship of belonging to a father, who loves us because we are His.