Federal headship is the theological term stating that a husband/father is the head, leader, and representative of his family. Adam was created first and set to rule over Eve, and this concept of the husband being the leader is found in both the Old and New Testaments. As part of Eve’s curse, she would have the desire to rule over her husband and usurp his authority. The mandate for Adam to be the head does not mean that he would be a dictator and Eve would be a subservient slave. That is not the case at all, for we know what God teaches us about marriage, especially in regards to how Adam is to love his wife like Jesus loves the church—unconditionally and with sacrifice.
Let’s apply this to Jesus. In the Garden of Eden, it was Eve who sinned first and Adam who sinned afterwards, but it is because of Adam that we are all under the curse of sin and death. Jesus, being the redeemer over the fallen creation, took the leadership role and responsibility to cover our sins by dying on the cross. His unconditional love saved us from our own created problem.