Because that is the formula, just like a2+b2=c2 is the formula used for other calculations.
—
Here’s the solution to the equation you are using:
y ≈ (c/2r)⋅x², where c = 63,360 in/mi,
r = radius of Earth in miles, r = 3982 mi.
c/2r = (63,360 in/mi)/(2⋅3982 mi)
c/2r = 7.96 in/mi² ≈ 8 in/mi²
So, y ≈ 8x² in/mi², for x << r,
where the units for x² is square miles (mi)², the equation for a parabola, not a good fit to a circle. The units for y is inches (in), because units are important.
This crude approximation fails for anything but for a local estimate.
Equation for a circle, radial components for a sphere,
x² + y² = r², r = 6,371 km