How many debates were involved?
With the Chalcedonan Creed many debates were involved. The Council was trying to address several popular heresies that had arisen.
That is the reason for the language of the creed.
Christ being "perfectly man" (completely human) and “co-essential with us” addressed the heresy of Apollinarianism - that Christ had a human body, a lower spirit, but humanity was just added to divinity (the heresy Christ was not fully human).
Christ being “co-essential with the Father” and “perfectly God” addressed Arianism. “two nature, indivisible, without mixture, immutable” addresses Eutychianism. “One person” “indivisibly, inseparably” addresses Nestorianism.
Not only is the Chalcedonan Creed a product of debates concerning the popular heresies involving the nature of Christ but it is a product of debates concerning the language used. The words “person” was a particularly “hot” debate.
The Athanasian creed may not have involved as much debate as it seems to be more of an expression of orthodoxy. But at least we can say that it stands on previous creeds and draws from the Chalcedonian Creed.