OK. Here is a guess.
How the needle moves depends on the compression of the round, flat cylinder within the ASI. At zero differential pressure, zero deflection. At x differential pressure, deflection is y. y=f(x).
There is no reason to assume the function f(x) is linear. Indeed it is more likely to be non-linear as the more compressed it is the more it's likely resist. This is the instrument maker's magic.