Practice what you preach is always sound advice, especially if one hopes to have any influence on others. This axiom is more than a moral exhortation and takes on legal significance regarding one of the best-known teachings of the Talmud. 
The Gemara (Kiddushin 29a) teaches that there are five, possibly six, obligations one has in raising one's son. These are to circumcise him, to "redeem" him if he should be a first-born Israelite (pidyon haben), to teach him Torah, to teach him a trade, to marry him off, and some say to teach him how to swim. 
In these six basic obligations we welcome the newborn into the Jewish community, educate him both religiously and generally, and continue the chain of Jewish history by marrying him off. Regarding the obligation to swim the Gemara's discussion consists of a mere two words[1]chiyuta hu, his life may depend on it. It is hard to imagine a more concise and important teaching especially in a world where almost everyone lived near the water. 
While these obligations rest with the parents, specifically the father, if one's father is derelict in his responsibility one must see to it that one fulfills these obligations oneself. Thus if the father does arrange for a pidyon haben, something that is most common today, the child must arrange for his own pidyon haben even years later. 
The Gemara has a fascinating discussion concerning the case where a grandfather did not do a pidyon haben for his son who now has become a father and must do a pidyon haben both on himself and for his son (perhaps only with the birth of his son is he made aware of his own personal obligation) but there is only enough money for one pidyon haben[2]. Should one take care of his father's obligation and redeem himself or should he take care of his own obligation and redeem his son?
Recognizing the extreme difficulty of performing a brit milah as an adult, most especially in the days before anesthetics, the Gemara places the obligation on the Jewish court to perform a brit milahshould the father not do so. Only if they too neglect their crucial responsibility must the son arrange his own circumcision as an adult. 
What is fascinating is that the Gemara records no obligation upon the mother for these mitzvoth. The Gemara explains that since there is no obligation upon the father of a pidyon habat there can be no obligation upon the daughter herself. And since she is not obligated to redeem herself there can be no obligation to redeem others. 
This logic applies across the board. With the mitzva of brit milahbeing inapplicable to women they cannot be the ones responsible to ensure their son is circumcised. 

We find similar logic regarding the obligation to teach one's children Torah. Since there is no obligation to teach a daughter [the non-practical aspects of] Torah a daughter is not obligated to arrange for someone to teach herself. And since she herself is not obligated she cannot be obligated to teach others.
While the Talmud does not specifically say so it appears this same logic also applies to marriage and a career. It is the husband's - and husband alone - responsibility to provide for the financial needs of the family. Thus it is he who must ensure his son can do the same for his family.  In a similar vein the actual obligation to have children is only incumbent upon men (see here for why this may be so) and thus they are the ones responsible to marry off their children.
This analysis may help explain why it is only "some" who say that a father must teach his son how to swim. As something necessary to protect oneself from potentially life-threatening situations, this would be an obligation that delves on fathers and mother towards both sons and daughters. It is not in dispute that all children must be taught how to protect themselves but rather a technical question of whether it should be included with the fatherly obligations. 
Of course while a woman may not be technically obligated in these mitzvoth it is hard to imagine a Jewish mother who in fact neglects these mitzvoth. What better example than Tziporah whose circumcision of her son prevented the death of Eliezer or possibly even Moshe. While the formal obligation rests with the father it is the mother who is often the driving force behind the children's development both religiously and in general. 
We conclude with the beautiful words of Rabbi Soloveitchik in his eulogy (see here for the full text) for his mechutanista[3], the Talne rebbitzen.
"One learns much from father: how to read a text - the Bible or the Talmud - how to comprehend, how to analyze, how to conceptualize, how to classify, how to infer, how to apply. . . . One also learns from father what to do and what not to do, what is morally right and what is morally wrong. Father teaches the son the discipline of thought as well as the discipline of action. Father's tradition is an intellectual-moral one..." 
"What kind of a Torah does the mother pass on?...I learned from her [his own mother] very much...Most of all I learned that Judaism expresses itself not only in formal compliance with the law but also in a living experience. She taught me that there is a flavor, a scent and warmth to mitzvot. I learned from her the most important thing in life - to feel the presence of the Almighty and the gentle pressure of His hand resting upon my frail shoulders. Without her teachings, which quite often were transmitted to me in silence, I would have grown up a soulless being, dry and insensitive."
[1] Sometimes it's best to keep the message short and clear. As we all know the aseret hadibrot consists of two "tablets" however the first side has many many more words than the second. As the Mabit, Moses ben Joseph di Trani, notes this would have the effect of ensuring commands such as lo tirzach, lo tinnaf and lo tignovwould be written in much larger font and hence be much more noticeable. It is for good reason our Sages teach kol hamoseef goreah, which is best paraphrased as whoever adds subtracts. 
[2] It seems clear from a variety of Talmudic sources that poverty was not at all uncommon. How sad that one lacks a few dollars for a pidyon haben - and sadder still that the Gemara has a discussion of what takes precedence when can't afford candles both for Chanuka and Shabbat (Shabbat 23b). With Pesach around the corner it is worth noting that the Mishna (Peschim 10:1) rules that even the poorest of the poor must be provided with four cups of wine; and the first ruling of the Rama in Hilchot Pesach (Orach Chaim 429:1) is that of maot chitim, ensuring all have the means to make a proper Pesach.
[3] The fact that the English language has no word for a mechutan speaks volumes of the different family dynamics between the Jewish and secular worlds. My son's in-laws just does not have the same ring.