It does have a shadow - but it is very faint. When you have a point source of light, it casts a strong shadow (which is really an image of the object casting the shadow). read more
It does produce a shadow, but it is very faint and thus creates an illusion of no shadow. A point source of light casts a strong shadow. As the source of light becomes larger then you end up with blurry shadow because it is made up of "lots of overlapping shadows" hence the edges seem blurry. read more
If you have a fluorescent tube, you can see that by holding a wide stick (maybe a cricket bat) parallel to the tube and close to the floor: now you will see a shadow as the tube is narrower in one direction. read more