Wayne Grudem wrote a fantastic book, SYSTEMATIC THEOLOGY, in which he addresses "why God created two sexes and whether or not they can be equal, yet have different roles". He discusses a lot of information of which I am only going to touch upon. I highly recommend reading the chapter in its entirety.
Grasping Marriage and the Rolls of Husband and Wife
27 For as many of you as were baptized into Christ have put on Christ. 28 There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus. (Galatians 3:27-28. ESV.)
Romans 13:14: But put on the Lord Jesus Christ, and make no provision for the flesh, to gratify its desires. (ESV.)
Galatians 3:14: so that in Christ Jesus the blessing of Abraham might come to the Gentiles, so that we might receive the promised Spirit through faith. (ESV.)
Galatians 5:6: For in Christ Jesus neither circumcision nor uncircumcision counts for anything, but only faith working through love. (ESV.)
1 Corinthians 12:13: For in one Spirit we were all baptized into one body— Jews or Greeks, slaves or free—and all were made to drink of one Spirit. (ESV)
1 Corinthians 11:11: Nevertheless, in the Lord woman is not independent of man nor man of woman; (ESV)
To clarify this, Grudem states,
Paul wants to ensure that men will not adopt some of the attitudes of the surrounding culture, or even some of the attitude of first-century Judaism, and think that they have greater importance than women or are of superior value before God. Nor should women think themselves inferior or less important in the church....
This equality is an amazing and wonderful element of the Christian faith and sets Christianity apart from almost all religions and societies and cultures. The true dignity of godly manhood and womanhood can be fully realized only in obedience to God's redeeming wisdom as found in Scripture." (1994. Zondervan. Pgs. 458 & 459.)
Dominate, Submit, or Contribute Nothing
3 But I want you to understand that the head of every man is Christ, the head of a wife is her husband, and the head of Christ is God. (1 Corinthians 11:3. ESV.)
Grudem explains this saying,
Just as God the Father has authority over the Son, though the two are equal in deity, so in a marriage, the husband has authority over the wife, though they are equal in personhood....
If tyranny by the husband and usurpation of authority by the wife are errors of aggressiveness, there are two other errors, errors of passivity or laziness. For a husband, the other extreme from being a domineering "tyrant" is to be entirely passive and to fail to take initiative in the family - ...
The corresponding error on the part of the wife, opposite of attempting to domineer or usurp authority over her husband, is becoming entirely passive, contributing nothing to the decision-making process of the family, and being unwilling to speak words of correction to her husband, even though he is doing wrong. Submission to authority does not mean being entirely passive and agreeing with everything that the person in authority says or suggests - it is certainly not that way when we are submissive to the authority of an employer or of government officials (we can certainly differ with our government and still be subject to it),... A wife can certainly be subject to the authority of her husband and still participate fully in the decision-making process of the family. (Pgs. 459 & 467)
Wrapping It All Up
In conclusion, Grudem writes,
Husbands, therefore, should aim for loving, considerate, thoughtful leadership in their families. Wives should aim for active, intelligent, joyful submission to their husbands' authority. (Pg. 467)
So, the husband and wife in their marriage are similar to the offense and defense of a college football team (Go Gators!). Though they have different rolls and responsibilities (plays), they are equally important to the success of the team (marriage).
(Oh, and when I think of "submission" to my husband, I do not see it as losing myself but rather giving (in love and wisdom) to him.)