Why do we say we believe in the “holy catholic church” in the Apostles’ Creed?
The Apostles' Creed is a statement of core Christian beliefs the developed initially as part of baptismal rites in the early church. The term "catholic" (with a lower case "c") did not and does not refer to any specific denomination or group of Christians. The term, etymologically, comes from two Greek words that together mean, "throughout the whole." "Catholic" in a single word, both means throughout all time and places and points to the essential unity or wholeness of the church in Christ. No one English term captures that dual sense of this ancient Greek word quite as well as "catholic." So when the creed states, "I believe in the holy catholic church," it refers to the wholeness of the whole church in all times and places rather than to any specific branch of Christianity.
For more, watch Liturgy Man's video that includes this topic.