why does rotational speed vary latitude?

Because the axis of rotation is through the NS poles. Which makes the radius of rotation, measured perpendicular from the axis, the radius of the planet at the equator but zero at each pole.

And we can write r = R cos(LAT) for the radius of rotation at any latitude LAT. R is the average or given radius of the planet.

So Earth rotates once each 24 hrs; thus its angular speed around the axis of rotation is w = 2pi/(24*3600) rad/sec. 2pi is once around in radians.

That makes the tangential speed on the surface of the planet to be V = wr = 2pi/(24*3600) * R cos(LAT) where the latitude is 0 at the equator and 90 degs at either pole.

EX: At the poles, LAT = 90 deg, the tangential speed on the surface is V = w R cos(90) = w R 0 = 0. And that results because there is no radius of rotation at either pole.

The points at the poles aren't moving at all. The equator has the largest radius, so it has the highest rotational speed.

If L = latitude, R = radius (miles), and w = rotational speed in revolutions/day, then the equation for speed at a given latitude is:

v = cos(L)*2*pi*R*w, in miles per day.