A graph of |magnetic flux density|, $B$, along the axis of a circular coil against displacement, $z$, from the centre of the coil is a bell-shaped curve (though not a Gaussian curve) with its maximum at $z=0$).
For two identical coaxial coils carrying equal currents in the same sense, the resultant B at a point, X, on the axis midway between the coils will be roughly constant for a short distance either side of X, because at X itself $\frac{dB}{dz}$ for one coil will be equal and opposite to $\frac{dB}{dz}$ for the other coil.
My last paragraph holds whatever the separation of the coils. But when we stray along the axis from X itself, in general $\frac{dB}{dz}$ will be different for the two coils so the change in B from one will not exactly cancel the change in B due to the other. BUT the cancellation will be much better if $\frac{dB}{dz}$ doesn't change much if we stray. So we choose X such that $\frac{d_2B}{dz^2}$ is zero. It turns out that $\frac{d_2B}{dz^2}=0$ is at a point along the coil axis half a coil radius from the coil centre.