Why does the mitzvah of joy specifically include those who may be left outside?
The Torah does not merely say, “Rejoice.” It specifies: “You shall rejoice on your festival, you, your son, your daughter… the Levite, the stranger, the orphan and the widow within your gates” (Deuteronomy 16:14). This is not private joy.
Maimonides writes that when a person eats and drinks on a festival he must also feed the stranger, orphan, widow and other poor people. A celebration that closes its doors to the needy is not the proper joy of a mitzvah (Mishneh Torah, Laws of Rest on a Festival 6:18).
That is a different definition of happiness. We usually ask: did I enjoy myself? The Torah asks: who enjoyed life because I was here? A beautiful holiday table can be full of food and still lack the most important thing: a place for someone who has no other table.
After Yom Kippur, when we asked for mercy, comes a festival that asks whether we learned to become merciful. Perhaps the size of our joy is measured not by how many people sat around the table, but by whether there was room for someone who was not sure he had anywhere to go.