NY wrote
Rod Speed wrote

Because there are more births on that day of the year
and so its statistically more likely that that will coincide
with the death day even if the deaths are evenly distributed
throughout the year. Which they arent in fact.

OK. So this all hinges on the fact that the birth rate (and maybe death
rate) varies throughout the year.

Yes, and all you need is the birth day to vary, the
death day doesn’t need to to get the statistical quirk.

If the same number of people were born on every date as on every other
date, you're saying that the increased probability of you dying on your
birthday would not be true?

Correct.

Now if the birth rate has a gradual peak at a certain time of year, more
people will be born at around that time of year. If there are more people
alive with a given birthday, does that automatically mean there there is a
greater chance that when a person dies (a fairly random event) their death
date will correspond with their birth date?

Like I said, ALL you need is an uneven number of births on particular days
of the year.

And why does the probability of any given person dying on a given date
have its maximum on *exactly* the same date as they were born - exactly as
opposed to "somewhere around their birthday".

I wonder if I will start to understand your reasoning.

Yeah, that will certainly be interesting to see.

Am I incredibly slow on the uptake

Not clear to me how common that problem is with basic statistics.

or are you especially insightful in understanding it?

It will be interesting to see how many others never get it.