The Haggadah says:
וַאֲפִילוּ כֻּלָּנוּ חֲכָמִים, כֻּלָּנוּ נְבוֹנִים, כֻּלָנוּ זְקֵנִים, כֻּלָנוּ יוֹדְעִים אֶת הַתּוֹרָה
Listing 4 different qualities means that each one is not sufficient, and those are not overlapping, but it sound weird, for example, זקן we know that stands for זה קנה חכמה, and includes two others.
What are those 4 distinctive qualities and why being חכם or זקן is just not enough?
These are 4 independent and orthogonal traits. Chochma symbolises our abilities to learn, bina is the capability of induction, daea is accumulation of knowledge and zikna is the perspective of time. Certainly all 4 are required traits for highly effective learning that is both meaningful and developmental.
It is symbolic in a sense, that mi yodea is a community in a meta-community of programmers.
The primary purpose of the Pesach Seder is to teach the story of the Exodus to the children. From this perspective, one could read the sentence as a metaphore said to a child, who is not interested so much, to convince him or her to follow the story. It also appears that the 4 qualities listed are necessary to make each of the sons of the hagadah interested. A parent hacham will interest the son hacham. A parent zakein will have patience with the rebelious son rasha. A parent navon, who can foresee the outcome, will be necessary to a son tam, who has tendency to completely be drawn into anything of interest. Finally, a person who knows entire Torah (at least in terms of the fundamental klalim), not just the one of the grown ups but also the one of the kids, will be necessary for the son who cannot ask to find what he wants or can get interested in.
Danny Liberman's description of the qualities is different from what R. Herszeg writes in "Patterns in Rashi". There, חכמה - collection of information (basic, scripture), בינה - ability to see differences (like Rashi's commentary, which can differ for similar things in different places), דעה - ability to see similarities (think Tosafos' commentary), entire Torah - probably everything noted repeated back and forth many times.
As far as the adults go, your question is based on the first half of the haggadah sentence, which further continues: And even were we all wise, all intelligent, all aged and all knowledgeable in the Torah, still the command would be upon us to tell of the coming out of Egypt; and the more one tells of the coming out of Egypt, the more admirable it is.
The qualities listed in the first part of the sentence are intellectual. The purpose of the Seder, though is not to split hairs, but rather to re-experience Exodus from Mitzraim as if one suffered as a slave of Pharaoh, saw the plagues, found strength to join the Jewish people grouped around Moshe, jumped into the split Red Sea, and finally experienced true freedom. Thinking about Exodus exclusively in intellectual terms does not impact one's heart. Furthermore, the words הֲרֵי זֶה מְשֻׁבָּח - it is praiseworthy at the end of the paragraph in the question raise the question, what is זֶה? I believe, Rashi states that זֶה means adding praise to Hashem, rather than getting enjoyment of intellectual discussion. The Hagadah is explicit about it:
GENERATION BY GENERATION, each person must see himself as if he himself had come out of Egypt, as it is said: “And you shall tell your child on that day, ‘Because of this the LORD acted for me when I came out of Egypt.’” It was not only our ancestors whom the Holy One redeemed; He redeemed us too along with them, as it is said: “He took us out of there, to bring us to the land He promised our ancestors and to give it to us.”
The requirement to experience the story of a Yom Tov is not unique to Pesach but it is an integral part of every Jewish holiday.
