Unless you were born Feb 29, I guess everyone's birthday is on the same day every year. Mine, for instance, is always on Sep 11, every single year.

You're confusing day (Monday, ...) with date (12th Dec).

He's pointing out that those stuck on a leap day are still stuck.

If you count by day-of-year when doing the conversion, though, it's the people born new year's eve on a leap year that are impacted.