What's the "lie," that Judaism is notoriously sexist, and that the Garden of Eden story sets up that sexism?

Adam is created to rule over the animal kingdom. Eve is created to serve as Adam's helper (2:18). Adam is created as an image of God. Eve is created to be part of man. Eve succumbs to temptation first. When their sins are discovered, Adam and Eve tell the plain truth: the woman that God put in Eden gave him fruit and he ate it. Genesis doesn't say that Eve told Adam it was the forbidden fruit (3:6). And Eve says she was "deceived" by the serpent. God punishes them by having women desire men and men ruling over women (3:16).

Where's the lie? Do you know how childish it sounds to call people you disagree with liars?

https://www.theguardian.com/commentisfree/belief/2009/jun/10/judaism-women-feminism-orthodox