A little halacha to start:
Chazal (B"K 82) tell us "ain mayim elah Torah" and darshen the pasuk in our parsha, "Vayeilchu shloshes yamim v'lo matzo mayim," as an allusion to the takanas Nevi'im (the Rambam says it was a takanah made by Moshe himself) not to go three days without public Torah study. We therefore lein on Shabbos, Monday, and Thursday.
Aruch haShulchan (135:5) says a chiddush that if for whatever reason the wrong parsha was leined on a Monday/Thursday, there is no need to do a makeup.
ולפי זה נראה לעניות דעתי דאף על גב דבשבת אם טעו וקראו סדרה אחרת דוודאי חוזרין וקורין הסדרה הזמנית, מכל מקום במנחה ובשני וחמישי כשטעו וקראו פרשה אחרת, מסדרה זו או מאחרת – אינם צריכים לחזור ולקרות. דכיון דאינה עולה לקריאת הציבור, שהרי בשבת הבא יקראוה מחדש, ולא נתקן אלא כדי שלא יהיו שלושה ימים בלא תורה, ומשום יושבי קרנות – ולכן בכל מה שקראו יצאו ידי חובתן. ואפילו אם נזכרו באמצע הקריאה נראה לעניות דעתי דמה שקראו – קראו, והמותר יקרא במה שנצרך היום לקרות.
It seems like there are two parts to his argument: a) we will hear the whole parsha anyway on the upcoming Shabbos; b) the takanah of leining on Monday/Thursday is very different from the takanah of leining on Shabbos. You have to read a specific sidra each Shabbos, but during the week the crucial point is that Torah be read publicly at least once every three days -- what you read is not important, so long as you read something.
Is the idea of not going three days without hearing Torah the geder of the takanah, or just the reason behind instituting leining on Mondays, Thursdays, and Shabbos? A possible nafkah minah might be the question of what to do if leining was missed on a Monday (quoted in Ah"S 135:7). If the geder of the din is to avoid a three day gap without Torah, then maybe leining should be made up on Tuesday, which would avoid the gap. On the other hand, if the takakah designated Monday and Thursday as leining days, then there are no makeups. Avoiding a three day gap is why the takanah was made, but does not define its parameters.
Secondly, a little machshava thought:
Did Bnei Yisrael, coming right off kriyas Yam Suf, really think that Hashem was going to starve them in the desert? That they would not have what to eat, and had to complain to Moshe for food?
The Sefas Emes teaches that a person can have all he/she needs to eat and yet still be hungry.
Baruch Hashem, I see in the newspapers ad after ad for Pesach hotels and vacations, but so many people who have so much these days are so dissatisfied with life. They have an endless hunger for more and more and are never filled up.
We know the navi tells us that at the time of redemption there will be a hunger, but not a hunger for food or drink, but a hunger for the dvar Hashem.
Bnei Yisrael had food, but they wanted more than gashmiyus food to fill their bodies with -- they wanted food that would also be dvar Hashem.
"Posei'ach es yadecha u'masbi'a l'kol chai ratzon" -- the Midrash notes that it doesn't says that Hashem is masbi'a with ochel, food, but rather Hashem is masbia and fulfills people's ratzon, desire. If your ratzon is just for a good meal, Hashem can give you that, but if your desire is for the dvar Hashem, then He will give so much more.
That's why Parshas Eikev, in describing what Hashem did for us in the desert, the Torah tells us, "va'yi'ancha va'yarivecha va'ya'achilcha es ha'mon," Hashem made us hungry and then gave us the mon to eat. Why does the parsha mention the hunger? That was the complaint, the problem. The pasuk should just tell us the wonderful thing Hashem did to solve the problem!
Sefas Emes answers that in this case, the problem was itself a bracha. By all rights we should have been happy to just have enough food. But we weren't. We had a hunger and desire for food that also would be dvar Hashem. That hunger could only be satisfied by the mon.
The Ch haRI"M teaches that on Tu B'Shevat it's decided what chiddushei Torah one will gain during the upcoming year. In other words, Tu B'shevat is not about filling up on dried fruits (or fresh fruits). It's about being hungry for Torah, for Eretz Yisrael, for ruchniyus things.