I guess another question is - how does this work if the father is the one with more education and is more qualified to teach the children than the mother and the father has to work all day? Teach in the evenings?

I suppose it depends what you mean by qualified, Vladimir.

My own experience is that one does not need to be "qualified" (in the formal sense) to teach. In fact I believe that being "qualified" can be an impediment, as "qualified teachers" have often been brainwashed and thus forced to follow the "right" way. Many of the teachers I know have a very limited perspective on life. After all, many go from the classroom as student to the classroom as teacher with little other experience of life.

In a sense being a mother one is a natural teacher. You just continue to do what you did for your child from infancy, adapting yourself to the needs of the child/ren at their various ages.

Just because the father "is the one with more education and is more qualified to teach the children than the mother" does not mean that the mother will not be able to do an adequate job of educating their children.

" and the father has to work all day? Teach in the evenings?"
Education continues in the home while ever the educators and educatees are awake. Although regular school hours CAN be a guide, they may not necessarily suit the family. That is one of the beauties of Home Education. It revolves around the family.

For example, if all the mother can really teach - from a purely academic perspective that is - is the basics of reading, writing, and a little arithmetic,

My experience is that that is all that is necessary. Our three, once they had "the basics of reading, writing, and a little arithmetic", were well equipped to study fairly indepenently, each following their own particular pursuits and talents.

whereas the father is well-schooled in the language arts, etc when will they have time to teach the children.

The first words that our first son heard, seconds after his birth, were those of his father, in his own languare which is not English. Since then our son has studied ancient and modern languages at University level.
 

However, I see that I've answered my own question and the more one thinks about it, the more beautiful homeschooling seems.

The way it revolves around the family seems very natural.

Got it in one!! The grace of the Sacrament of Marriage is a big part of it. Marriage is for the procreation and EDUCATION of our children.

Sadly the SSPX have a very negative view of Home Schooling. This affects many SSPX homeschoolers here and they seem to think of it as something you must do if you don't live near a SSPX school. Seems a real shame.

What is most needed is encouragement to parents (and support for mothers) to discover that, with the Grace of God through the Sacrament of Marriage, they can do it (in most cases).