When a baby is born, it's easy to see the average age of the population decreases.
Intuitively, therefore, when a person dies, the average age of the population must increase to compensate.
However, this isn't always true. If the person who dies is above the average (mean) age, the average age actually decreases (I'm ironically omitting the math but can provide it on request).
This also applies to the median age: both births and above-average-age deaths decrease the median.
The only way to increase the mean/median age is when a person dies before reaching the mean/median age.
This seems really counter-intuitive. We expect most people to die AFTER they reach the mean/median population age.
Is there an intuitive way of understanding this?
You just have to realize that the average age of the population always increases as the time flows!
So it's not really odd it decreases they way you describe. In fact it has to.