The Jewish calendar is not purely lunar. It is lunisolar — adjusted periodically so that the festivals fall in their proper seasons. The Mekhilta traces this practice of calendar adjustment all the way back to a single verse in (Exodus 23:15): "The festival of Matzot shall you keep."
Rabbi Yehudah ben Betheira zeroed in on the key phrase: "as I commanded you, at the appointed time in the month of Aviv." The month of Aviv is springtime — the season when barley begins to ripen in the Land of Israel. The Torah does not merely say to observe Passover. It says to observe Passover in the month of Aviv. The festival must coincide with spring.
But a purely lunar calendar drifts about eleven days each year relative to the solar seasons. Left uncorrected, Passover would eventually fall in winter, then autumn, then summer — cycling through every season over the course of roughly thirty-three years. The Torah's insistence that Passover occur in Aviv makes this unacceptable.
The solution is intercalation — the periodic addition of an extra month to the year. When the rabbinical court determined that Passover would otherwise fall too early, before the barley had begun to ripen, they added a second month of Adar, pushing the entire calendar forward and ensuring that Passover landed in spring.
Rabbi Yehudah ben Betheira derived this entire system from the Torah's precise language. The phrase "at the appointed time in the month of Aviv" is not a poetic description of the season. It is a binding legal requirement that compels the court to intervene in the calendar itself whenever nature and the lunar cycle fall out of alignment. One verse, and from it, the entire Jewish calendar takes its shape.