tefilla - Why does the date for the prayer for rain change from one century to the next?

My due diligence:

I see that I’m walking into a “duplicate question” minefield. So if you’ve got an answer, answer quickly.

Suppose that we use the word “summer” to refer to that part of the year when the northern hemisphere has relatively warm weather, long days and short nights; and we use the word “winter” by contrast to mean that part of the year when the northern hemisphere has relatively cold weather, short days and long nights.

If we do all of that math described in all of those previous questions and conclude that in one century we will begin to pray for rain on December 3, and in the next century we will begin on December 4, and in the next century we will begin on December 5, is that because December is moving from winter to summer, or because our prayer for rain is? Or is there some third alternative?

In other words, I'm not asking how to compute anything. I'm asking what these computations are supposed to achieve, and what they will achieve. In what sense will this set of rules (our complicated rule for this prayer and the complicated rule concerning February 29) preserve the seasonality of our prayer and of the months January through December?