“And Adam called his wife’s name Eve; because she was the mother of all living.” Gen 3:20 KJV
There are two senses (or more) in which Eve be called the mother of all living. A traditional reading of Genesis 1 would deny the existence of other people outside the Garden. Adam calling Eve the mother of all living is used to try and prove all humanity descends from Eve by some eg Ron Cowie and Phil Perry.
“If there were other humans in existence then Adam was sorely mistaken in thinking that his wife was the mother of all living humans. Would God have allowed that deception to go unanswered?”
This is an inconsistent approach to scriptural interpretation, as the same brethren claim phenomenal language to explain difficulties in Genesis 1, but here attribute complete knowledge to Adam – or demand God explain everything to Adam. God clearly didn’t explain many things, and accommodated misunderstandings consistently in Scripture. The argument is adopting an inconsistent approach to scriptural interpretation for the purposes of trying to condemn other believers.
Adam’s pronouncement can be read quite faithfully another way. Adam and Eve had just received the judgment for their sin and also in Gen 3:15 the promise of a seed who would resolve the enmity with the serpent. We rightly understand the passage as a promise about the seed of the woman – the Messiah. In a very real sense life would come through Eve. Adam in naming his wife is recognising the promise. This is not a new interpretation but stated by brethren who explicitly rejected evolution eg Bro H Whittaker “The emphasis on “mother” underlines Adam’s faith in the promised Redeemer, the seed of the woman.”. HP Mansfield commented the phrase “revealed his [Adam’s] faith in the promise made”. It would be pleasant to also see in the expression a maturation of Adam. Having previously attempted to shift blame to Eve in Gen 3:12 he has the grace to embrace her in a positive light now. There’s an example for my marriage and possibly others…
 Cowie, Ron (2015) “Why we believe what we believe” Study 4, 21 min 30.
 Perry, Phil (2016) “Theistic Evolution Refuted” version 1.9 page 18
 Whittaker, H. Gen 1-2-3-4 Biblia, page 109 (1986)
 Mansfield, HP Key to Understanding of the Scriptures. Logos Publications (1997), electronic edition