Aircraft windshields and windows are made from a hard durable MIL standard acrylic plastic that has a long service life. However, they are still plastic and can be damaged if not cleaned properly. Aircraft windshields and windows are not only expensive, but changing them takes a lot of expensive labor. Paper towels are made from a matrix of processed wood fibers that can be hard enough to scratch plastic. Paper towels will not damage the acrylic every time they are used, but consistently using them will eventually give you little fine scratch defects that refract light differently than an adjacent smooth surface. The small differences in light refraction will obstruct and distort your view.
Dust is made up of many little abrasive particles so it is important to isolate the dust particles from the windshield as you wipe. The softer and more expanded the cloth material is, the greater the tendency for the cloth to absorb the dust particles isolating them from the cloth surface. In other words, the dust particles can go deeper into a soft fiber matrix as compared to a harsh hard fiber matrix of paper towels. Dust and dirt particles tend to collect on the hard paper towel surface giving it a sandpaper effect. Gently feel a paper towel surface. Gently feel a T-shirt or micro fiber cloth. The surface hardness is very noticeable.
In summary, there are really two differences in a paper towel and a soft fiber cloth. One difference is the hardness of the actual fiber and the second is the ability of the fiber matrix to absorb dust particles away from the fiber surface.