Man is commanded to teach his children Torah. It is not enough that he learns Torah, goes out to shul and keeps mitzvos – he must verbally express his love for Hashem and His Torah in order for his message to get across.
Women are different. The woman’s entire being emanates her emuna.  Emuna is represented by the letter “mem” and we see that in every language, the word for mother always contains the letter “mem” – mummy, ima, mere, mama…etc. Whatever she is will be passed on into her children. And that is why Judaism is always passed on through the mother.

She is “mother earth”. She is the roots of the earth. She does not need to “teach” her children Torah, whatever she is will seep into her children from her own roots.