If you go to about 4:05, he says this:
That you will let your voices be heard, we cannot, we cannot meet our destiny as the Church of Jesus Christ of Latter-day Saints in preparing this world for the 2nd coming of the Savior of the world without the support and the faith and the strength of the women of this church. We need you. We need your voices. They need to be heard. They need to be heard in your community, in your neighborhoods, they need to be heard within the ward council or the branch council. Now don’t talk too much in those council meetings, just straighten the brethren out quickly and move the work on. We are building the kingdom of God.
I can think of three ways to interpret his counsel not to talk too much:
1. It was a joke. He seems to smile after saying it and we in the church don’t speak in serious tones of women “straightening out the brethren.” If this is the best reading, I’m caught between two reactions:
a. It’s not a good idea to joke about hot-button issues, especially ones where some people are deeply emotionally invested and/or troubled.
b. It’s a good idea to reduce tension by using humor, especially when it comes to hot-button issues.
But I have to admit that, when it comes to what you want to model for the general church membership, joking about hot button issues is probably on the What Not to Do list, especially if your speaking style is such (as I think Elder Ballard’s is) that it is not entirely clear if you are joking.
2. He was completely serious that women should not speak too much in council settings. This sentiment seems to align with a quotation from him published in this month’s Ensign:
Now, sisters, while your input is significant and welcome in effective councils, you need to be careful not to assume a role that is not yours. The most successful ward and stake councils are those in which priesthood leaders trust their sister leaders and encourage them to contribute to the discussions and in which sister leaders fully respect and sustain the decisions of the council made under the direction of priesthood leaders who hold keys. (cite)
I have previously expressed concern that the approach of Ordain Women would lead to retrenchment and backlash. Given Elder Ballard’s previous support for women’s leadership in the church, a theme he emphasized strongly in his book Counseling with our Councils, I would say that these two statements reflect a desire to encourage women to stay within the boundaries of current church practice regarding leadership roles, at least partially as a response to OW.
3. He was saying, in effect, “don’t spend a lot of time talking about things. Your voice is important but your actions are more important. Even if you have to correct male leaders, get the job of building the kingdom done.” This is not a gendered message that women should not talk a lot; it is rather a general statement that no one should waste words when they could instead deliver their message and then get to work. That his statement appeared to be directed specifically to women is an unfortunate accident. The fact that he gave women explicit permission to correct males in council settings is a big win for those advocating for a greater role for women in the church.
I’m honestly not sure which is the best reading; it seems like you can make a decent case for each of them. I don’t envy anyone who has to speak to an international audience that will parse every word and facial gesture. I join with Joseph Smith in praying that we will someday be delivered from “the little narrow prison almost as it were tot[a]l darkness of . . . a crooked broken scattered and imperfect language” (cite).