But you can also say: "Do you know what 11:59PM means? 12:00PM is one minute after that"

Midday and midnight are the points at which AM/PM change and you can't logically differentiate them by appending AM or PM. You just have to know the arbitrary cultural convention that midday is PM.

The underlying observation is that the entire hour from X:00 - X:59 is either AM or PM, and not a mixture.

12:00 and 12:01 are both in the 12:XX hour, but 11:59 and 12:00 are not. Of course the whole thing is arbitrary, but the convention is that the 12:00 - 12:59 hour is PM, rather than just 12:00.

I think, though, that your example is less convincing, since the hour changes.

> 12:00 AM is one minute before that.

Which is strange, because it does not follow the concept that all other of those time"stamps" do.

12 AM implies that 12 hours of something has passed, but it's nothing that we would align our lives against. And why is 11 AM after 12 AM on the same day? There's no logic (ok, some, but... well... a strange one) behind that.

This is only ok as a way to know. The person could then argue "so one minute before 12:00 AM is 11:59 AM, right?" If the person's not familiar with the convention, it makes sense.

The problem with that explanation is it doesn't make it more logical that 12:59am is one minute before 1:00am.