In a similar way to that in which the Pharisees sought to find precedents in the lives of the Patriarchs for their own innovations, Jubilees tries to trace reasons for the Jewish festivals, which God does not give in the Torah (beyond the fact, which is of secondary importance in Judaism, that they are associated with agricultural events), to the lives of the ancients.
In this case, at issue is the date of שָׁבוּעוֹת (Shāvuoth, Pentecost). Nowadays, this celebrates the Giving of the Torah at Mt Sinai, but this association did not exist in Temple times. Rather, it was invented afterwards as a means to justify the continuation of the festival once the Temple had been destroyed, and it was no longer possible to offer its requisite sacrifices.
However, this reason would not have been available at all to the author of Jubilees, because of their differing interpretation of Leviticus 23:15:
Leviticus 23:15 ויקרא כג טו-כג טו You shall count for yourselves from the morrow after the sabbath, from the day that you brought the sheaf of the wave offering; seven sabbaths shall be complete: וּסְפַרְתֶּם לָכֶם מִמָּחֳרַת הַשַּׁבָּת מִיּוֹם הֲבִיאֲכֶם אֶת־עֹמֶר הַתְּנוּפָה שֶׁבַע שַׁבָּתוֹת תְּמִימֹת תִּהְיֶינָה׃
Two thousand years ago, this was the subject of sectarian divisions between the Pharisees, who interpreted "the sabbath" here as the first day of Pesach, and the Saducees and Boethusians, who interpreted it as the first sabbath after Pesach. I've become convinced that in their opposition to everything the Saducees stood for, the Pharisees here threw away the baby along with the bathwater, and that the seven weeks of the Omer were indeed measured from the sabbath after Pesach. This would have made שָׁבוּעוֹת fit in with the other two Pilgrimage Festivals and occur at full moon.
At any rate, the author of Jubilees would have certainly gone with the "sabbath after Pesach" interpretation; and here is the justification he places in the mouth of the angel for the date of שָׁבוּעוֹת:
[God] gave to Noah and his sons a sign that there should not again be a flood on the earth. He set His bow in the cloud for a sign of the eternal covenant that there should not again be a flood on the earth to destroy it all the days of the earth. For this reason it is ordained and written on the heavenly tablets, that they should celebrate the feast of weeks in this month once a year, to renew the covenant every year. This whole festival was celebrated in heaven from the day of creation till the days of Noah—twenty-six jubilees and five weeks of years; and Noah and his sons observed it for seven jubilees and one week of years, till the day of Noah's death, and from the day of Noah's death his sons did away with it until the days of Abraham, and they eat blood.
But Abraham observed it, and Isaac and Jacob and his children observed it up to thy days, and in thy days the children of Israel forgot it until ye celebrated it anew on this mountain. And do thou command the children of Israel to observe this festival in all their generations for a commandment unto them: one day in the year in this month they shall celebrate the festival. For it is the feast of weeks and the feast of first fruits: this feast is twofold and of a double nature: according to what is written and engraven concerning it, celebrate it.
One of the other divisions between the Pharisees and the Qumran community was the nature of the calendar. For the Pharisees, and their spiritual descendant, rabbinic Judaism, the calendar is lunisolar, based on the sighting of the new moon (with leap months intercalated every two or three years, to keep it synched with the solar year, unlike the purely lunar Islamic year, which creeps forward eleven days each year). For the Qumran community, by contrast, this was rank heresy; they believed that the true Jewish calendar had always been solar, and laid out in a highly structured order. Jubilees continues by laying out this order and its justification in the time of Noah:
On the new moon of the first month, and on the new moon of the fourth month, and on the new moon of the seventh month, and on the new moon of the tenth month are the days of remembrance, and the days of the seasons in the four divisions of the year. These are written and ordained as a testimony for ever; Noah ordained them for himself as feasts for the generations for ever, so that they have become thereby a memorial unto him. And on the new moon of the first month he was bidden to make for himself an ark, and on that (day) the earth became dry and he opened (the ark) and saw the earth. And on the new moon of the fourth month the mouths of the depths of the abyss beneath were closed. And on the new moon of the seventh month all the mouths of the abysses of the earth were opened, and the waters began to descend into them. And on the new moon of the tenth month the tops of the mountains were seen, and Noah was glad. And on this account he ordained them for himself as feasts for a memorial for ever, and thus are they ordained. And they placed them on the heavenly tablets, each had thirteen weeks; from one to another (passed) their memorial, from the first to the second, and from the second to the third, and from the third to the fourth.This looks like it's talking about new moons, but it's not, it's just the terminology for the first of each month, as becomes clear from its continuation below, which is incompatible with a lunar calendar:
And all the days of the commandment will be two and fifty weeks of days, and (these will make) the entire year complete. Thus it is engraven and ordained on the heavenly tablets. And there is no neglecting (this commandment) for a single year or from year to year. And command thou the children of Israel that they observe the years according to this reckoning—three hundred and sixty-four days, and (these) will constitute a complete year, and they will not disturb its time from its days and from its feasts; for everything will fall out in them according to their testimony, and they will not leave out any day nor disturb any feasts. But if they do neglect and do not observe them according to His commandment, then they will disturb all their seasons and the years will be dislodged from this (order), [and they will disturb the seasons and the years will be dislodged] and they will neglect their ordinances.
(It is thought that they did not actually observe a three hundred and sixty-four day year, which would get out of sync pretty quickly; IIRC, once a while they would have a week which was not counted as part of the year, which would get everything back into sync.)
The above passage then leads into a rant against the Pharisees who,
with their lunisolar calendar are causing the Israelites to sin by
celebrating the wrong days as yomtov, and that this will lead
mixed dancing eating blood:
All the children of Israel will forget and will not find the path of the years, and will forget the new moons, and seasons, and sabbaths and they will go wrong as to all the order of the years. For I know and from henceforth will I declare it unto thee, and it is not of my own devising; for the book (lies) written before me, and on the heavenly tablets the division of days is ordained, lest they forget the feasts of the covenant and walk according to the feasts of the Gentiles after their error and after their ignorance.
For there will be those who will assuredly make observations of the moon: how (it) disturbs the seasons and comes in from year to year ten days too soon. For this reason the years will come upon them when they will disturb (the order), and make the day of testimony an abomination, and an unclean day a feast day, and they will confound all the days, the holy with the unclean, and the unclean day with the holy; for they will go wrong as to the months and sabbaths and feasts and jubilees. For this reason I command and testify to thee that thou mayst testify to them; for after thy death thy children will disturb (them), so that they will not make the year three hundred and sixty-four days only, and for this reason they will go wrong as to the new moons and seasons and sabbaths and festivals, and they will eat all kinds of blood with all kinds of flesh.
In 1 Enoch it is made clear that the practice of setting the calendar by observations of the New Moon was a practice taught to humanity by the Watchers, and part of their corruption of humanity.