I shall answer the scripture in context, out of the King James version. 1Cor 11:3 is quoted here, and used out of context to belittle women (and I think this is one place where Paul mistook what Jesus said):
1 Be ye followers of me, even as I also [am] of Christ.
2 Now I praise you, brethren, that ye remember me in all things, and keep the ordinances, as I delivered [them] to you.
3 But I would have you know, that the head of every man is Christ; and the head of the woman [is] the man; and the head of Christ [is] God.
4 Every man praying or prophesying, having [his] head covered, dishonoureth his head.
5 But every woman that prayeth or prophesieth with [her] head uncovered dishonoureth her head: for that is even all one as if she were shaven.
6 For if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered.
7 For a man indeed ought not to cover [his] head, forasmuch as he is the image and glory of God: but the woman is the glory of the man.
8 For the man is not of the woman; but the woman of the man.
9 Neither was the man created for the woman; but the woman for the man.
10 For this cause ought the woman to have power on [her] head because of the angels.
11 Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord.
12 For as the woman [is] of the man, even so [is] the man also by the woman; but all things of God.
As you can see, it only tells about women wearing something on their heads to pray and prophesy--not that they cannot run for assignments like passing the microphones. And even that is coming from a former Pharisee, who errantly took Christ's words literally. I challenge anyone to actually find something that Jesus said that belittled women explicitly--to repeat 1Cor 11:1, it tells people to become followers of Paul even as he is of Christ.