nah, not a weird word.

Also, if there would shine light on top of a pillow, and you are viewing from top too, there would actually be realistic pillow shading.

Try it out with your pillow!

Also, pillows are mostly soft and smooth objects. Pillowshaded objects look soft and smooth too right?

Pillow shading comes from a Photoshop filter where a certain layer/image will have a depth added from the center in/out and was centered. This filter is no longer in Photoshop but has evolved to one called bevel/emboss.
When pixelart was kinda a new thing and images were shown where lighting was head on someone (unknown) called it Pillowshade from the Photoshop tool and it has stuck over time.
The reason pillowshading is seen as a negative is because that PS tool did not analyze the image to produce depth at all and merely based the FX based on outline shape.

As with anything, there are always exceptions to the rules. The may be occasion where pillow shading is acceptable. For example, if you make a GUI and it contains lights behind a button, then the light emitating would be centered and thus pillow shaded.