The only place in the New Testament where the word "authority" (exousia) is directly connected to gender/sex is in 1 Corinthians 7:1-7. This "authority" has nothing to do with the husband bossing his wife around. This passage says that neither the man nor the woman has "authority" over their own body, but that their spouse does. In verse five, it says "Do not deprive one another [of conjugal rights], except perhaps by agreement for a limited time, that you may devote yourselves to prayer; but then come together again, so that Satan may not tempt you because of your lack of self control." In other words, the husband cannot unilaterally announce, "We are going to be physically separated for awhile." Such an action should only take place if they mutually agree on it.
It is said that "If this is the case in an important issue like physical separation, one would assume that the goal in marital decision-making is for the couple to be one-minded." The idea that 1 Corinthians 7:5 "throws a wrench into the works for those who would conclude that the husband has the 'final say'" is just nonsensical. The context is marital conjugal rights. It is said that unless husband and wife can mutually agree on decisions, that they should do nothing. Well, there is a colossal problem with this kind of logic (or lack thereof), and it is also false.
What if the wife is on her way to earning her tenure, and the husband gets offered work in another state or country? If they talk about it and do nothing because they cannot agree, then essentially they have made a decision and they have chosen her course of action because they are staying there. Or, an extreme example, what if the husband and wife are in the middle of the highway and he wants to get off the road and she wants to continue standing in the middle of it? If they do nothing because they cannot agree, then her course of action has been chosen and they will both die. Where there is already an investment in the decision to be had, by not doing anything you are siding with the existing investment and continuing down that road. Only if neither party has an investment does the "do nothing" work: He wants to eat at A&W and she wants to eat at McDonalds.
Ask anyone who has a horse-drawn carriage or a dog sled or any other team-oriented practice and the answer will be exactly the same. While all horses in a horse-drawn carriage pull the same weight and move at the same speed, there is always a lead horse. Always! While all dogs in a dog sled pull the same weight and move at the same speed, there is always a lead dog. Always!
As with any theological difference of opinions, the truth is always somewhere in the middle, and the debate between Complementarianism and Egalitarianism is no different. Yes, when 1 Corinthians 11:3 talks about being the 'head,' the Greek word literally means "source." It has nothing to do with authority. While men and women are equal in the eyes of the Lord as far as dignity and worth (they are not absolutely equal as men will always be faster and stronger than women), and while they should be a team that tries to pull the same weight and move at the same speed, nevertheless there is always going to be a lead. Scripture makes it clear that this lead is to be the man. However, this "lead" does not mean half of what Complementarians would suggest that it means.
In Ephesians 5:22, wives are told to "submit" to their husbands. This submission is not blind, and we should also have an understanding as to the Greek word used. Hupotasso has both a military and non-military use. The military use has a connotation of being "subject to" or "to obey" as if you are under someone's command. Most people think of this meaning. The non-military use means "a voluntary attitude of giving in, cooperating, assuming responsibility, and carrying a burden" (Thayer's Greek Lexicon, #5293). In ancient papyri, the word commonly meant to "support," "append," or "uphold." The wife's responsibility is mentioned in verses 22-24 and 33. The husband's responsibility is mentioned in the 7 verses in between, and likely has more to say to the husband than to the wife because of how the first century often viewed women as property.
If you want to discover the truth on this issue, the issue between Complementarianism and Egalitarianism, you are going to find it in the middle. Examine both, look at the merits and faults of both, compare them honestly with Scripture (in context), and then form your beliefs. Do not force Scripture to side completely with either system because it will not work for you.