Malbim Ayelet HaShachar Klal 544
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וזה הטעם ששביעי של פסח ושמיני של חג נקראו בשם "עצרת", ולא יום הראשון של פסח וסוכות ויום טוב של שבועות. כי ימי חג האחרונים נקראו "עצרת" בערך ימי חולו של מועד שלפניהם שנאסרו גם כן בקצת מלאכות וביום טוב צריך להעצר מכלל מלאכה. (אמור ס' קפז)
And this is the reason why the seventh day of Passover and the eighth day of the Feast of Tabernacles are called עצרת and not the first day of Passover, the Feast of Tabernacles, and the Feast of Weeks: The last days of the festival are called עצרת, since during the weekdays of the festival before them, some creative activity is also prohibited, while on Yom Tov one needs to עצר (halt) from all creative activity.
The holiday of Passover has seven days. On the first day, all creative activity is prohibited. And then from the second day to the sixth day, called Chol HaMoed, only some creative activity is prohibited. Finally, on the seventh day, all creative activity is prohibited. This is calledעצרת.
Similarly, the Feast of Tabernacles has eight days. On the first day, all creative activity is prohibited. And then from the second day to the seventh day, called Chol HaMoed, only some creative activity is prohibited. Finally, on the eighth day, all creative activity is prohibited. This too is calledעצרת.