Major festivals in several traditions move against the civil calendar each year. The reason is that they are dated by the moon, and lunar dating solved a problem no solar calendar could.
The moon is observable without any authority
A lunar month begins with an observation anyone can make. No instrument, record or central announcement is required to know roughly where the month stands.
For dispersed communities without reliable communication, this was the only basis on which distant groups could keep the same dates.
Solar calendars require accumulated astronomical knowledge and an institution to maintain them, which not every community had access to.
Lunar and solar years do not divide evenly
Twelve lunar months fall short of a solar year by roughly eleven days, so a purely lunar calendar drifts backwards through the seasons.
Traditions that accept the drift have festivals that move through the whole year over a few decades, occurring in every season in turn.
Traditions that require festivals to stay in season insert an additional month at intervals, which keeps the lunar months aligned with the agricultural year.
Agricultural anchoring drives the intercalation
Festivals tied to harvest, sowing or the spring must stay in their season, and an unadjusted lunar calendar would carry them into winter.
Intercalation rules therefore exist to hold particular festivals in place, and the rules are usually justified by reference to those specific observances.
The resulting calendars are lunisolar, and they are considerably more complex than either pure system because they are reconciling two.
Observation versus calculation is a live question
Traditions differ on whether a month begins when the new moon is actually sighted or when calculation says it should be.
Sighting keeps the original practice and introduces variation, since cloud cover and geography mean different communities see it on different evenings.
Calculation produces certainty and allows dates to be published years ahead, which matters for scheduling but departs from the practice as it was performed.
The moving date is part of the observance
A festival that arrives at a different point each year cannot be treated as a fixed seasonal fixture, and communities watch for it rather than assume it.
Preparation begins from an announcement or a sighting rather than from a diary, which involves the community in establishing the date itself.
Where dates have been fixed to the civil calendar for administrative convenience, that participatory element disappears, which is a recurring point of disagreement within traditions that have done it.