The count of whole-degree “lines” of latitude (the poles, the equator, and those in between) is indeed 181 . Of course that is because there are 360 degrees in a circle. Now the count of whole-degree lines of longitude is 360 …so why does latitude differ?
On a sphere (which our planet nominally is) all points are created equal so the difficulty is how to orient oneself. Fortunately the Earth spins (fairly stably) on an axis so we have its poles to use as a reference. Thus evenly-spaced lines of longitude were devised which pass through those poles: 360 of them…easy peasy.
That accounts for one dimension of the sphere’s two-dimensional surface, but what about the other one? One might manufacture two more “poles” equidistant from the real ones. But, boy, what a mess of grid lines that would make! A much better solution was to have evenly-spaced parallel circles which shrunk in size as they approached each pole: the lines of latitude. Now if one were to traverse a line of longitude all the way around the world one would cover 360 degrees of latitude. However that counts each (non-pole) latitude twice so the “proper” count is the aforementioned 181 .
But then, one may ask, why are there 360 degrees in a circle? Well, blame the Babylonians. There are two schools of thought as to exactly how that number arose.