From a mathematic standpoint, February 29 occurs between February 28 and March 1. If the 28th passes directly the 1st, that moment is the same moment that people born on the 29th have their age counter go up, which happens without having a birthday (in the sense of 'this part of the year is your birthday').
From an astronomic standpoint, there aren't 365 or 366 days in a year, but 365.256363004 days in each of earth's revolutions around the sun, and creations (even rocks have birthdays too, not just life forms!) on earth should have their birthdays wobble back and forth by a calendar day based on when in the day they were born. Fun fact, a year as a unit of time is about 20min shorter than a revolution because it is based on the solstices and equinox(es?), which are infulenced by axial precession. By the way, what is the plural of equinox? I feel like I should pronounce it the same as singular, but maybe an -es or an -s gets tacked on when written?
What? Why are you sad Ms. Agentt? I must have used too many commas; that one sentence needed a semicolon instead. I'm sorry Lady Keeper of Periods and Commas.