Why does one need to LEAN OUT a CARB when climbing?

Couple followups to the responses on this thread.

First, I'm not doubting that you have to lean at higher altitudes; that
is empirically most true. I'll try to restate the question below...
Stealth Pilot wrote:

"why do I lean my carb when I climb" is a bull**** question open to
much misinterpretation.

"why do I need to lean my carburettor at higher altitudes" is probably
a better wording of the question.

Sure, that's what I was asking in the original post.

that is simple. the air is less dense so the amount of fuel it needs
to achieve full combustion is reduced. the density of the fuel doesnt
decrease so you need less of it.

That I understand. It's also effectively a handwaving explanation to
the original question.

Here's the original question restated. Can somebody explain, why at
higher altitudes, the less dense air does not automatically meter less
fuel through a carb venturi, automatically making up for this
difference. A carb venturi operates taking advantage of the decrease in
pressure associated with the increase of velocity through the venturi --
a phenomenon which is dependent on the density of the air.

This question doesn't apply to a fuel injected engine, where as I
understand the fuel metering volume does not depend on air density, or
to any carbs with a compensating device.