When you stop to think about it, Pesah Sheini is a very strange holiday, with a motivation that would be incomprehensible for almost any other festival.  As we read in Bemidbar 9, some people were ritually impure on the 14th of Nisan—the eve of Pesah—and therefore unable to perform the foundational mitzvah of slaughtering and eating a paschal offering.  They ask for a second chance, and God grants it: On the 14th of the following month, Iyyar, they may slaughter their lamb.