A childhood belief about birthdays

At the beginning of the year my Mom showed us kids when our birthdays were by marking them on the calender. My older brother's birthday was in January, my birthday was in February, and my younger sister's birthday was in March.

Based on this evidence I believed that everyone older than me, but younger than my brother, must have their birthday sometime between his January birthday and my February birthday. Similarly, someone younger than me, and older than my sister, had a birthday sometime between our birthdays. Those younger than my sister had birthdays later in the year.

I was so convinced this was true that I had even taken the effort to figure out how there could be so many people who were older than my brother, even though there were very few days in the year before his birthday. As I figured it, once all the possible birthdays had been used up, January birtdays started again (which would take a long time based on the time required for birthdays to advance one month). This conveniently explained how my parents could have birthdays in the summer- they were way older than me, so they were on a different birthday cycle. My siblings and I were just lucky to have birthdays so early in the cycle.

I found out this was not true after being invited to my neighbor friend's birthday party. I knew she was a year younger than me, but her party was in early February- before my Birthday!!! I tried to tell her she had her birthday wrong, but she wouldn't listen. Her mother had to break up the fight and explain how age and birthdays really worked.