Kesubos, Chapter 4, Mishnah 6. The Mishnah opens with a ruling: "Ha'av eino chayav bimzonos bito" - a father is not obligated to provide food for his daughter. As we mentioned a few Mishnayos ago, a father is not required to support his daughter during his lifetime. After his passing the matter changes, since a daughter's support is included among the conditions of the kesubah: one of the conditions of the kesubah is that the daughter is supported from the estate. But as long as the father is alive, by strict law he is not required to support his daughter, and likewise his sons once they have reached the age of six and older.
The obligation as a matter of tzedakah:
Even though there is no obligation from the laws of support, there is a duty upon him from the mitzvah of tzedakah. The Rambam writes, based on the Gemara, that a person who does not want to feed his children after the age of six - even though technically he is not obligated - is shamed, and public measures of embarrassment are taken against him until he understands to do so. And if the court has determined that he is a man of means, he is compelled even by actual coercion to spend money for their support, as part of the mitzvah of tzedakah that rests upon him.
The derashah of Rabbi Elazar ben Azaryah:
The Mishnah continues: "Zeh midrash darash Rabbi Elazar ben Azaryah lifnei chachamim b'kerem b'Yavneh" - this exposition was stated before the Sages, at the time when the Sanhedrin sat in Yavneh. The basis of the derashah lies in two conditions established in the enactment of the kesubah: "habanim yirshu v'habanos yizonu" - the sons shall inherit and the daughters shall be supported:
"Habanim yirshu" - this is the condition of kesubas benin dichrin: the sons inherit their mother's kesubah. When there are sons from two different mothers, each group of sons inherits its own mother's kesubah.
"V'habanos yizonu" - the daughters are supported after the father's death, and their support is paid from the estate.
From here Rabbi Elazar ben Azaryah expounded: "Mah habanim einan yorshin ela l'achar misas ha'av, af habanos einan nizonos ela l'achar misas avihen" - just as the sons inherit their mother's kesubah only after the father's death, so too the daughters are entitled by law to support only after their father's death. The relationship of the sons to the kesubah parallels the relationship of the daughters to their support: both take effect only after the father's passing.
In summary: in this Mishnah we learned that by strict law a father is not obligated to support his daughter during his lifetime, and this law is derived from the derashah of Rabbi Elazar ben Azaryah, who compared the support of the daughters to the sons' inheritance of their mother's kesubah - both apply only after the father's death. However, all this is by strict law alone; from the standpoint of the mitzvah of tzedakah, the father is shamed publicly until he feeds his children, and if he is a man of means he is even compelled to do so.