JOEL - If your son is a member of the church I hope he was just teasing his grandmother and was not really serious about what he said. I assume he is getting this idea from the following scripture in Genesis:

"Unto the woman he(God) said, I will greatly multiply thy sorrow and thy conception; in sorrow thou shalt bring forth children; and thy desire [shall be] to thy husband, and he shall rule over thee." (Gen. 3:16)

The best answer to this question is found in the Proclamation on the Family from the First Presidency of the Church:

"Each is a beloved spirit son or daughter of heavenly parents, and, as such, each has a divine nature and destiny. Gender is an essential characteristic of individual premortal, mortal, and eternal identity and purpose.
By divine design, fathers are to preside over their families in love and righteousness and are responsible to provide the necessities of life and the protection of their families. Mothers are primarily responsible for the nurture of their children. In these sacred responsibilities, fathers and mothers are obligated to help one another as equal partners."

So, according to the First Presidency husband and wife are equal partners, each responsible for their own specific duties. Even though the husband presides over the family, this does not mean that he is more important, it is simply one of his responsibilities as a priesthood holder. These gender-specific roles are eternal principles that have always existed and always will exist.
However, men and women can take on different roles if the circumstances neccesitate it.
The proclamation I refered to also states: "Disability, death or other circumstances may necessitate individual adaptation." There are many single parent families that require a man or woman to take on nontraditional roles. It may not be the ideal situation for proper development for the children, but if that parent is doing the best they can they will be blessed for it.
And many women in LDS families do obtain advanced education and have careers in many fields. There is nothing wrong with this as long as the children and family do not suffer because of it.
The scriptures tell us how equally important the man and woman are to each other in regards to their eternal life:

"Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord."(1 Corinthians 11:11)

"In the celestial glory there are three heavens or degrees; And in order to obtain the highest, a man must enter into this order of the priesthood [meaning the new and everlasting covenant of marriage]; And if he does not, he cannot obtain it." (D&C 131:1-3)

And according to President Spencer W. Kimball:
“The women of this Church have work to do which, though different, is equally as important as the work that [men] do. Their work is, in fact, the same basic work that we are asked to do—even though our roles and assignments differ.
We have all been blessed with special women in our lives—women who have had a deep and lasting influence upon us. Their contribution has been and is most important to us and is something which will be of everlasting value to us”
(in Conference Report, Oct. 1979, pp. 71-72; or Ensign, Nov. 1979, p. 49).

Husbands and fathers are more important in the specific roles they must perform. But Wives and mothers are also more important in their God-given roles. But the man is not more important than the woman.