It is not commanded in the Bible or hallowed as a yom-tov in the Talmud.
We observe it because it spontaneously expresses the Jewish love of the Divine word.
The name Simchat Torah (literally, “Rejoicing of the Torah”) says, “Jewish people, rejoice in the Torah!” It also says, “Torah, rejoice in the Jewish people!”
Is it enough for a husband to love his wife unless the wife also loves her husband? Is it enough for a parent to love their child unless the child also loves its parent? Love unrequited is hardly love.
Hence on Simchat Torah the question is not merely whether we feel like dancing with the Torah but whether the Torah feels like dancing with us.
Maybe that is why Simchat Torah comes at the very end of the whole long cycle of festivals; the succession of celebrations renews our acquaintance with Judaism and when we dance with the Torah we are not like strangers who hardly know or remember each other.