I think 'head covering' is taken way out of contrast - it shouldn't be taken literally as Paul was addressing one specific cultural difference in one specific cong., and it had to do with shaven-headed women - reformed/converted prostitutes if I remember right.
I think his words about women being silent are taunting(sarcastic), not literal. If he meant what he said about men and women and Jews and Gentiles being equal in God's eyes, then he can't have meant that he literally didn't 'allow' women to teach. There were deaconesses and women teachers - it was the men who had pride problems with it.
Could be wrong, but that's my take on it.