Can't you subtract it from 90

The argument of a complex number $z = x + yi$ is defined as the angle $\theta$ that the line segment from the origin to the point $(x, y)$ makes with the positive real axis in the complex plane, measured counter-clockwise.

The formula $\arg(z) = \arctan\left(\frac{y}{x}\right)$ (with quadrant adjustments) directly calculates this angle $\theta$.

Subtracting an angle from $90^\circ$ would give you its complementary angle, which is the angle with the positive imaginary axis, not the positive real axis. This is not the standard definition of the argument of a complex number.

For example, with $z = 2 + 3i$:
The argument is $\arctan\left(\frac{3}{2}\right) \approx 56.31^\circ$.
If you were to subtract this from $90^\circ$, you would get $90^\circ - 56.31^\circ = 33.69^\circ$. This $33.69^\circ$ is the angle the complex number makes with the positive imaginary axis, not its argument.