Did God err in making Adam ruler over Eve?

Scripture are clear. Sin and death entered this world through Adam, and he was thus to blame for original sin.

Yet God rewarded Adam with dominion over Eve even though Eve was not responsible for sin and death entering the world. Gen3:16 and thy desire shall be to thy husband, and he shall rule over thee.

This shows God continuing the policy of punishing the innocent instead of the guilty that is shown in scriptures. 1Peter 1:20 He was chosen before the creation of the world, but was revealed in these last times for your sake.

God seems to be rewarding Adam for sin while punishing Eve for the events in Eden even though she was innocent of sin as she did not have any evil intent and was deceived by Satan, a force that she could not possibly resist thanks to God giving Satan the power to deceive the whole world after God put Satan in Eden with Eve.

If making man ruler over women that was an error, it would help explain the 5,000 years of war we have had to endure with undeserving men as rulers.

Gnostic Christianity, a Universalist belief system, believes in full equality for all souls. Christianity obviously does not believe in equality if it preaches that men are to perpetually enjoy ruling over women. Not to mention the inequality of gays.

Did God err in making Adam ruler over Eve and thus punishing the innocent instead of the guilty?

Regards
DL