TL

“Is God’s reaction to Adam a sign that Adam now has a sin nature that makes him untrustworthy? The fact that God drives only the man out of the garden shows that he possesses a rebellious sin nature that will be passed on to us. ”

They both sinned. But interestingly, the rebellion and treachery was what made the difference. Besides failing to honor and love God it was a failure to act on important information that would benefit Eve. The treachery was twofold. Adam dishonored God and dishonored the woman that God gave to him as the help for his aloneness.