A rotary fibrous insulation product that is soft to the touch is provided. The fibrous insulation product is formed of glass fibers having an average fiber diameter less than about 5.5 microns. The low fiber diameter helps to impart a soft feel to the insulation product. Additionally, the insulation product contains an oil with a flashpoint of at least 580° F. in an amount up to 5% by weight of the insulation product. The insulation product may contain up to about 85% by weight recycled glass. In exemplary embodiments, the binder is a low-formaldehyde, polyacrylic based binder. The combination of the low fiber diameter, the binder, and the oil create a synergistic effect to produce an unexpectedly soft insulation product. The insulation product is useful in a variety of thermal applications, such as in basements, in attics, and in walls of residential dwellings.