Why does Pastor Armstrong switch between using Eve or Woman when discussing Adam's wife?
In the account of Creation, the original name of Adam's wife was Woman:
Adam later changed her name to Eve after the Lord made atonement for their sin:
Whenever Pastor Armstrong makes reference to Adam's wife, he uses the name in effect at that moment in history. Specifically, before the moment of atonement in the Garden, her refers to her by her first name, Woman, and after the atonement, he calls her by her second name, Eve.
Pastor Armstrong generally follows this principle with all biblical characters. For example, when discussing events of Genesis 17 and earlier, Paster Armstrong refers to the first patriarch of Israel as "Abram." After Chapter 17, he refers to the man as "Abraham" reflecting the man's new name.
To understand the significance of Adam changing the name of his wife, please listen to our Genesis study available here: Genesis – Lesson 3D