The eating of the forbidden fruit, made Eve wise and like God, knowing the difference between good and evil, obedience and disobedience.
Satan is the one who says this, while deceiving Woman. ((Genesis 3:5))
God doesn't say the man & the woman have become like Him -- He says the man has. ((Genesis 3:22))
and He doesn't say it when it is confessed that they have eaten, but after He pronounces judgement, when Adam changes the name of Woman to Eve. Genesis 3:22-24 speaks of 'the man' in singular, not plural.
the right interpretation fits the text. the right interpretation fits with what God says, not what Satan says.