Just look at picture #2 . Spokes from opposite flanges cross paths.
Take,for example, the near flange heads up spoke at 12 o'clock.
The spoke in the far flange is in the flange hole immediately clockwise from the near spoke, but traverses to the rim
hole immediately COUNTERclocksise of the referenced spoke.
The paths visually cross right about at the diameter change of the spokes.
Obviously the stagger is incorrect for a true radial pattern.
Had the spoke in the far flange been laced to the hole immediately clockwise to the reference spoke,
the paths would be parallel and result in a true radial lacing pattern.

Simple.