According to HowStuffWorks, fiberglass is safe when installed properly. Upon installation, the tiny fibers settle between panels, sheetrock, and plaster. The fibers become airborne when the insulation is removed.
Fiberglass insulation contains tiny fibers of glass that can irritate the skin, explains HowStuffWorks. Too much contact with the skin can cause contact dermatitis or inflammation of the skin.
There is a misconception that fiberglass and asbestos are the same material, HowStuffWorks notes. The only commonality between fiberglass and asbestos is that they are both fibrous. Asbestos is a natural silicate material found in rocks, while fiberglass is a man-made material. Asbestos can withstand high temperatures and doesn't evaporate in the air or water, qualities which made asbestos a popular option for insulating homes in the late 19th and early 20th centuries.
HowStuffWorks warns that when released into the air, asbestos fibers separate into microscopic pieces. These undetectable fibers are easily inhaled and stick in the lungs for long periods of time. The health problems associated with asbestos, which include mesothelioma and other cancers, do not show up for 10 to 40 years. As far as fiberglass insulation is concerned, The American Conference of Governmental Industrial Hygienists has labeled fiberglass as "not classifiable as a human carcinogen."