So in your opinion, upon what are the distinctions rightly based?
I believe the distinctions are revealed throughout the Scriptures, in God's own definitions and descriptions of Himself. A sample passage would be the inspired definition and description of the promised Christ Child promised in Isaiah 9:6-7.
Do you agree with this statement?: "It is the Father who generates, the Son who is begotten, and the Holy Spirit who proceeds." This summary is virtually the fullest extent of the distinctions between the three divine persons, as far as I can tell.
I agree that this describes the divine economy as it relates to creation, but I am not sure it is ontological distinction within the Godhead.
Where do you see this in their teachings on the Trinity?
In the sentence just discussed that appears to be premised upon ontological differences, origins, and actions. . . which I do not see revealed as occurring in the eternal realm.
I believe the individuations of Father, Son, and Holy Spirit, remain the only "I AM."
Edited to add: I am not arguing. Just discussing my take on the wording of the catechism.