Abayei said (Shabbos 21b) that he wished he had learned the din of kavsa ain zakuk lah earlier in life and not only in his later years. Asks the gemara: What difference does it make if you learned the din then or learned the din now -- as long as you know the din? Answers the gemara, the difference is girsa d'yankusa -- what you learn as a child sticks with you.
Why is it davka here, in the middle of the sugya of Chanukah, and nowhere else in sha"s, that an Amora bemoans not having learned a din earlier in life?
The Kozhiglover explains that the lesson of kavsa ain zakuk lah is that it's not the effect produced by having candles burning or how long they burn which is significant, but rather it's the initial act of lighting which defines the mitzvah. Chanukah is about beginnings -- the rededication of the Mikdash, the first lighting of the menorah in the Mikdash. So long as you get off on the right foot, no matter what happens afterwards, you've have accomplished something.
The Achronim (see R' Yosef Engel in Gilyonei haShas) explain that even through tumah hutra b'tzibur and a pure jug of oil would ordinarily not be necessary to light the menorah when everything is tamei, nonetheless, when it comes to chinuch hamikdash there is no din of hutra or dechuya, i.e. when it's the first lighting that we are talking about, it must be done without shortcuts.
Therefore, it is precisely in this context of Chanukah that the gemara stresses the importance of girsa d'yankusa, what we accomplish in learning and avodah when we are young and what we put into our children so that they can grow in Torah when they are young. The initial steps in our chinuch make all the difference.
(I have had an impossible day at work and don't have anything important to say about the parsha yet.)