The “Catholic Church” as we know it today out of “Rome” did “not” exist during St. Ignatius of Antioch’s time.
He was referring to “all churches” (hence the meaning of the word “Catholic” which literally means “Universal”) toward all churches which existed at that time (primarily in the East), such as Alexandria and Syria too.
In fact, St. Ignatius himself is of Antioch (and not Rome). Catholicism as we know it today gained power (“militia wise”) to establish itself as a theological centre instead only after the emperor Constantine embraced Christianity.
Before that, the Eastern churches were the “theological centres” and it’s a well hidden fact from history that out of these “first theological schools” of Christianity, the majority “correct” doctrine was “Christ centred Universalism” (taught in the “original Greek” language used in New Testament Scripture as opposed to Rome’s Latin mistranslations especially of the word “forever”).
Here is the historical quote:
“Early Christianity and that in the first five or six centuries of Christianity, there were six known theological schools, of which four (Alexandria, Antioch, Caesarea, and Edessa) were universalist, one (Ephesus) accepted conditional immortality (or annihilation) and one (Carthage or Rome) taught the endless punishment of the lost.”