There's several ussues with this argument:

- If the interference pattern was explained by diffraction by a semi-infinite plane, why don't I see it when using only one finger? I only see a blurry shadow. The second finger is needed to make the pattern appear.

- All formulas that are used compute the light intensity projected on a screen. In the actual experiment, we're looking at the slit through a lens (our eye or a camera). That's not the same thing.

- The fact that this is white light interference is handwaved away. To model it correctly, you'd need to compute what happens at each wavelength, then integrate the resulting spectrum multiplied by CIE's x, y z functions at each point, and finally do a bunch of math to bring that in the sRGB color space if you want to display the model's result on a screen.