What could be the cause of inverted nipples?

Multiple causes. Some women have naturally inverted nipples. If the nipples are normally everted and become inverted, there is more concern. One common cause is repeated episodes of infection/inflammation (periductal mastitis) which over time causes scarring and nipple inversion. Breast cancers also can result in nipple inversion/retraction. Therefore it is important to have an evaluation by a breast specialist.
Various. Inverted nipples occur due to variety of causes. These can be broadly classified as congenital (present since birth) or acquired (that develops later during the lifetime). Acquired conditions are:   breast abscess, breast cancer, recurrent infections, or prior breast surgery. Most are without complication, and even with invert. Nipples there are techniques to help breastfeed.