Jesus is a wonderful example of having total equality with the Father and yet there is no conflict ref submission and headship. It is a beautiful way to honour, love and trust. The world would never understand this, as equality means having the same power, same money, same rights etc.
It is incredible how far culture and the scriptures are apart from each other now but I guess it is not surprising and I find we are in a constant battle in so many areas. One example in my life is 1Cor 11 and head covering for women. It was done until the mid 60s when our culture allowed it. But now it is very unfashionable and unpopular, I try to wear something that is culturally as appropriate as possible. It's not so easy but seeing how fiercely the truth about divine order, headship and submission is attacked by the enemy, I am grateful to be a quiet reminder to the truth of God's word.